The three most important aspects of riding both comfortably and efficiently will always be positioning, positioning and positioning. It stems from frame geometry, and you should never underestimate the value of proper bicycle fitting.

Once you have the right bike, you can work on posture:

Arms: Keep your elbows bent and relaxed to absorb shock and prevent veering when you hit a bump or brush another rider. Hold arms in line with your body, not splayed to the side, to be more compact and aerodynamic.

Upper Body/Shoulders: Don’t be rigid, but do be fairly still. Imagine the energy wasted by rocking side to side with every pedal stroke on a 35k ride. Save it for pedalling. Also, beware of creeping forward on the saddle and hunching your shoulders, as there’s a tendency to do this when pushing for more speed. Keep your shoulders back and down to open your to Shift to a higher gear and stand periodically to prevent stiffness in your hips and back.

Head and Neck: Resist the temptation to put your head down when you’re going hard or getting tired. It takes just a second for something dangerous to pop out of nowhere. Occasionally tilt your head to one side and the other instead of holding it dead centre. Change your hand location to reposition your upper body and give your neck a new angle.

Hands: Prevent finger numbness by moving your hands frequently. Grip the bar firmly enough to keep hands from bouncing off on unexpected bumps, but not so tightly that it tenses your arms. For the same safety reason, keep your thumbs wrapped around the bar instead of resting on top. Move to the drops for descents or high-speed riding, and the brake lever hoods for relaxed cruising. On long climbs, grip the top of the bar to sit upright and open your chest for easier breathing. When standing, hold the lever hoods lightly and sway the bike side to side in synch with your pedal strokes, directly driving each pedal with your body weight. Generally speaking, drop your elbows and relax your hands.

Back: A flat back is the defining mark of a stylish rider. Notice I didn’t say a great rider. Anatomy and flexibility have a lot to do with how flat you can get. Lance Armstrong, for instance, has a rounded back that’s not picture perfect and yet he still manages to go down the road pretty well. The same was true for John Howard, once America’s dominant road racer. I’m in their boat (back-wise, not speed-wise).

Once you have the correct reach, work on flattening your back by imagining touching the top tube with your belly button. This helps your hips rotate forward. You don't want to ride this way all of the time, but it'll help you get more aero when you need to.

Feet: Some of us walk like pigeons, others like Charlie Chaplin. To make cycling easier on your knees, shoe cleats must try to put your feet reasonably towards their natural angle. Clipless pedal systems allow feet to pivot freely (“float”) several degrees before release, all you need to do is set the cleats’ fore / aft position. Position them so the widest part of each foot is centred on the pedal axle. If you experience discomfort such as tingling, numbness or burning (especially on long rides), move the cleats rearward as much as a centimetre.

Butt:  By sliding fore or aft on the saddle you can bring some muscles into play while resting others. Moving forward emphasizes the buttocks and quadriceps in the front of the thighs, while moving back highlights the hamstrings and glutes (the powerful butt muscles) as well as giving a bit more leverage on the pedals.

Injury-free pedalling.

In cycling the use of proper equipment and correct technique is essential for comfort, safety, performance and injury prevention, and the use of appropriate shoe gear when cycling cannot be overemphasized. Maintaining a sustainable cadence with low resistance is key to the correct pedalling technique, which will enable you to ride further, with less fatigue and strain on the joints and muscles. 

• Pedalling is about spinning, not stepping. An excellent way to become a better cyclist is to practice a shuffle-like pedal action. Instead of focusing on how fast or far you are riding, try to focus on maintaining a cadence of 80-90 RPM's - whilst staying within your target heart range – adjust your gears to maintain it. Don’t drop below 60rpm as you lose the fluidity of the pedal stroke.
• Pull & push. Try to maintain a smooth pedal stroke ("pedal in circles"). Don't just "mash" down on the pedals during the down stroke, neglecting the bottom - and upstroke. Spread the energy utilized throughout the stroke. Although biomechanical studies have shown that you don't really ‘pull up’ on the pedal on the backstroke (although you may think so) it does create fluidity in your pedalling and aids efficiency. Accordingly, when a pedal reaches 6 o'clock pull back with the trailing foot and simultaneously push with the front foot.  After a while you'll pedal smoother enabling you to apply more power, through more of the stroke.
• Ankling. Some older authorities recommended the practice of "ankling”, which refers to changing the angle of the foot fairly drastically during the course of the pedalling stroke, so that the toe is pointed downward at the top of the downstroke, and upward at the bottom upward pulling stroke. The idea is to vary the use of the calve muscles, and to permit "pedalling in circles", i.e., applying more force to the cranks at top and bottom dead centre. This practice is fairly discredited these days, and if carried to an extreme can cause injury, but can rest sore muscle groups when used. 

Exercises in pedalling.

• Ankling. Despite what is said above ankling can help in working towards the perfect "pedalling in circles" technique. Use it – with discretion - to focus on your calves, or to rest other muscle groups.
• Going it single. There are exercises for improving pedalling, such as doing single-leg workouts on an indoor trainer. Warm up with the bike in an easy-to-spin gear. When you're loose, pull one foot out of the pedal and rest it on the trainer. Now pedal for thirty seconds to a minute trying to be as efficient as possible with your one leg. Pedal easily with both legs for one minute, and repeat the exercise with the other leg. Or find a quiet road, unclip one foot, hold it out to the side, and pedal with the other leg.
• Rev it up. Another good exercise can be performed both on the road and on a trainer. A cyclo-computer with cadence helps with this, or count how many complete revolutions you make with one foot in 6 seconds, and then multiply by 10 to get your rpm (revolutions per minute). Put your bike in a low gear and take your cadence up to 120 rpm and hold for 30 to 45 seconds. Try hard not to bounce and concentrate on staying smooth and supple. Take a short break to recover and repeat 4 times during your ride. Keep in mind this a technique drill and not an interval, so be sure to gear down enough that you aren't straining to hold your target cadence. Doing one or two reps is a great way to complete a warm-up.

Climbing

Climbing is most affected by weight and the lighter you are the faster you'll be able to go. Combining proper breathing with high-cadence circular-pedalling whilst riding your own pace, is the key.
A simple guideline to start off with is to climb “ in the saddle" if a hill is long, and to stand if it’s short. It becomes a matter of preference depending on your ability, but always climb at your own pace, ride easy and stay strong.

• Gearshifting. By shifting gearing ratios you are able to maintain your comfortable cadence for longer. Sustaining cadence tempo is more attainable at lower rpm (eg. 60 rpm) and remaining within a comfortable zone is key. Try not to “shift down” too soon as valuable momentum will be lost, but at the same time do not shift too late as you might waste energy by working too large a gear ratio, needlessly burning your legs. Shift often - you can carry downhill momentum further up the hill when maintaining a steady cadence by shifting often. The key is to plan ahead, and not to let ego limit your gear ratio!
• Standing.   (En danseuse: from the French, "dancing on the pedals,"  “pumping” or pedalling while standing up). It is possible to stand out of the seat and pedal by using a relatively “high” gear, thereby resting the primary muscle groups, and in doing so to tap from reserve muscle groups allowing a burst. Careful with too low a gear ratio! The drawback in standing is that your aero efficiency is greatly reduced, but its all relative, as you’ll be climbing at reduced speed mitigating the additional dragging. Keep a relaxed touch on the bars with the hands, and the shoulders and the torso open to allow for maximum breathing. No bouncing! Standing is smart for when you need a break, when you are nearing the summit or when you need to accelerate, as the leverage gained in pulling on the handlebar allows a higher gear ratio.
• Sitting.  A taller person will benefit from sliding to the front of the saddle, positioning their hips over the crank to give them more leverage as demanded by the increase of the gradient of the incline. For a smaller individual, sliding back on the saddle helps to generate more force and power throughout the pedalling stroke. Use a lighter gear than if you were to stand, and spin up that hill with a comfortable cadence pedalling in a smooth, round stroke (best on a long hill). Use those glutens!
• A combination of the two. By changing your position from sitting to standing and back, you stretch the back and change the muscle groups used and are able to rest one set while relying on others for a while. On a long hill you may sit most of the way and only stand when it gets steeper, or to pick up the pace for a burst.   

Goofy-footed coasting

When you coast with the cranks in a horizontal position, ideally you should have the left foot forward, right foot rear. This way the stresses on the crank/bottom bracket interface are in the usual direction. If you coast with your right foot forward, that's sometimes called "goofy footed" and can even contribute to loosening up the crank since it applies stress in the opposite direction than the stresses of normal pedalling. This term comes from the world of surfing, where left-foot forward is the norm.

Chainrings.

There has been development into shaft driven bicycles, but the ‘cog & chain’ drive remains the most effective. With a chain-driven bicycle the possibility exists to vary the mechanical advantage of pedalling according to the position of the cranks, by using elliptical and non-round chainwheels.

Elliptical Chainrings. The idea centres on the fact that the large radius of the elliptical chainwheel can 'drive' the chain when the cranks are horizontal, with the small radius 'pulling' the chain when the cranks are vertical. As a result you will be able to 'push a higher gear' when the cranks are vertical whilst you are reaping the benefit of a smaller radius of the chainwheel during the 'dead spot' in pedalling motion. Accordingly - so the argument goes - the pedalling stroke becomes (overall) more efficient.

It has always looked great in principle, but does not work in practice. The high gear (with the cranks being horizontal) encourages the rider to push too hard - a common cause of knee problems - and the low gear (cranks being vertical) means that the knees are moving extra fast when they are changing direction (from going up or down (the "whiplash" effect).

Over time elliptical chainwheels have been re-invented and abandoned - for the same reason - every ten or fifteen years.

Shimano's Biopace™ was a patented, computer-aided 'non-round' chainwheel design. It might look like a traditional elliptical chainring, but it's not. It works diametrically opposed to the traditional elliptical chainwheel, as the small radius of the chainring is engaged when the cranks are horizontal, the large radius when the cranks are vertical. The Biopace™ design is based on analysis of the motion and momentum of moving cranks and legs, unlike the static, geometric analysis that produced the first elliptical chainrings.

The theory behind Biopace™ is that during the power down-stroke - the cranks being horizontal - you are using the power of your legs to accelerate your feet and the momentum of your feet, legs and cranks can carry you through the "dead spot" (when the cranks are near vertical). Since the rider doesn't push as hard during the power phase of the stroke, and motion is slower when the leg is changing direction, the Biopace™ design is gentler on the knees than a normal chainwheel!

Generally speaking, the slower motion at top and bottom means that as legs change direction from upward to downward/ vice versa, they will do so at a slightly slower speed. The increased leg speed near the middle of the stroke is the result of a more gradual acceleration / deceleration with the leg moving in the same direction. Thus, as Biopace makes it easier on your knees, it may also help you 'spin' better without bouncing, as 'bouncing in the saddle' results from changes in the legs' direction.

Biopace™ chainwheels are particularly suitable for touring cyclists / any application that involves a steady, constant cadence. They allow efficient pedalling at slower cadences than what is possible with round chainwheels. They are especially suitable for triathletes (the motion of 'transition' is a little bit closer to that of running, making it a bit easier) and mountain bikers (the design somewhat smoothes out the delivery of power to the rear wheel) as traction can be increased. Non-round chainwheels are of real value for the majority of non-racing cyclists.

It is possible to mix Biopace™ and round chainwheels on the same crankset - usually a small Biopace™ chainwheel  coupled with a round bigblade - taking advantage of Biopace’s™ superior (climbing) performance at low cadence, whilst having the ‘big blade' available for flatland spinning.

Shimano has discontinued Biopace™ chainwheels.

It should also be noted that within the bicycle industry the term "biopace" has come to represent slang for any "new product" which revolutionizes a certain aspect of cycling, yet - on closer inspection - does not perform as advertised!

Bicycling aerodynamics.

Research seems to have shown that: 

•  Time trialing is about efficiency, not really power, and it's almost easier to increase efficiency rather than power.
• Your bike accounts for only 15-20% of overall drag, with 75% of drag being determined by your body's resistance.
• There is a relationship between biomechanics, power output and aerodynamics. You have to balance all 3 to maximize power output over time.
• A non-aero helmet creates four times the drag of a non-aero wheelset.
•  How the race number is fixed to the bike matters - make it as flat as possible against the bike – as the drag created by an improperly affixed number can create more drag than the benefit derived from an aero wheelset!
• On a round-tubed bike frame a water bottle on the seat tube is more aero, than without.
• Wearing gloves creates more drag than the benefit reaped in having an aero frontwheel!

Basic Aerodymamic principles.

While bicycles are being designed with better aerodynamics in mind, the human body is simply not intended to "slice through the air", and cyclists  have relatively poor aerodynamics.
 
Aerodynamic drag consists of differences in pressure and viscous shearing stresses caused by the bicyclist moving through air. The viscosity of air is relatively small - but not negligible – and responsible for two types of drag, being frictional - and pressure drag.

Frictional drag comes from friction between the airflow and the surfaces exposed to the airflow. It arises from the fact that air (and other fluids) has viscosity. Direct friction occurs when wind comes into contact with the outer surface of the rider and the bicycle. Racing cyclists often wear "skin suits" in order to reduce such "direct friction".

Pressure drag comes from the eddying motions that are set up in air by the passage of the rider. This part of the flow is called the "wake" and is similar to the flow left behind a passing boat. Low-pressure regions form behind the object and result in a pressure drag against the object. The high pressure in  front and low pressure behind the cyclist  literally pulls him backwards. Streamlined designs aim to help the air close more smoothly around the body, and reduce pressure drag.
Frictional drag is less of a factor than pressure drag. On a flat road, pressure drag is by far the greatest barrier to a cyclist's speed, accounting for most of the resistance felt when pedalling. The only greater obstacle is climbing a hill, and the effort needed to pedal a bike uphill against the force of gravity far outweighs the effect of wind resistance. 

Frame builders and designers have been working on creating more aerodynamically efficient designs, and there is a delicate balancing act between maintaining a good strength-to-weight ratio while improving aerodynamic efficiency. Improvements to wheels have, perhaps, made the biggest impact. 

A standard spoked wheel (an "egg beater") creates many small eddies as the wheel rotates, creating drag. Disc wheels, while generally heavier than their spoked counterparts, produce less wind drag and turbulence when they spin, and contribute substantially to aero improvement. Yet, while improvements to frames and components have improved aerodynamic performance, the cyclist itself remains the largest obstacle. 

Body positioning is vitally important and road cyclists must reduce their frontal area, which in turn reduces the amount of resistance to be overrcome that helps increase speed and efficiency (over time). In addition to positioning, details like clothing also make a difference in reducing frictional drag, but drafting remains the most important aero technique in road racing. 

Drafting

Improve the aerodynamics of airflow and you reduce the overall drag (both surface - and separation drag.

In road racing, bicyclists group together in a pack known as a "peloton" or pace line / "echelon." Cyclists who are part of the group can save up to 40 percent in energy expenditure, over a cyclist who is not drafting within such echelon. To be effectively drafting, a cyclist needs to be as close as possible to the bicycle in front of him, as the shorter the distance the larger the decrease in wind resistance. 
 
In mountain biking, drafting is less important. The speeds are slower (than road racing) but it does help to keep pace with someone ahead of you. Besides the slower speeds, the twisting up-and-down nature of mountain biking courses renders drafting virtually  irrelevant. 
 
In recumbent design the cyclist pedals from a seated position which gives the bicycle a lower profile, and incorporates fairing around the vehicle which is substantially more aero efficient. Recumbents have been around for over 100 years, and hold a number of speed and endurance records (the world record holder in the 200 meters travelled at 110 km/h) simply as a result of their aero efficiency. The most advanced bicycles today, however, are deployed in track racing.

A rider riding solo "creates several drag inducing vortices" as well as low-pressure cavities that “suck him backward”. A trailing rider however, alters the pattern of the front rider’s wake’s vortex and low-pressure area behind him. In drafting  the vortex's anomalies straighten out, and the front rider’s pedalling effort becomes an estimated 3% easier as a result of the symbiotic relationship. In addition, a four man pace line requires an average of only 75% of the power of an individual at the same speed, as the brunt of wind resistance of the pace line is absorbed by the rider in front. At race speeds in a pace line it would seem that it is 17% easier for the 2nd rider, 38% easier for the next, and 40% for the 4th position on the back, and the leader fronting the echelon has a 3% “wake straightening” benefit than if cycling by himself.

A four man pace line can cover the same distance at a higher speed with a lesser percentage of effort. This is in fact the case, as the four man 4000m time trial record is more than 10 seconds faster than the individual 4000m record, with less average watts used! 

“Wheelsucking actually make tandems go faster!”