The three main considerations are comfort, power production and aerodynamics. You must choose a balance of these three elements in order to achieve your optimal fit. Determining the right balance for you should be based on a variety of individual characteristics such as the type of cycling you do, competitive level and experience, muscle imbalances or previous injuries, and your personal biomechanics and riding.
Comfort First
Comfort comes first, even for a competitive cyclist. If you're uncomfortable you can't produce power, period.
I've observed novice cyclists in very aggressive aerodynamic positions with a low power output resulting from being in an uncomfortable position. By putting them in a less-aggressive position, they were actually faster because they could pedal harder.
Comfort, of course, is relative. A time trialist must make sacrifices in comfort, but they'll spend a relatively short period of time on the bike.
If you're new to cycling there's an acclimation period in which your body adjusts to spending more and more time in the saddle. Some discomfort is normal, but cycling shouldn't be painful. If you're experiencing joint, back or neck pain, it's time to look at your fit or perhaps your pedaling mechanics.
Saddle soreness or numbness should be addressed immediately. These issues can often be relieved with a different saddle type or a simple adjustment.
Type of Cycling
Next, I consider the type of riding the cyclist will do. If you're a recreational rider, comfort should be your primary consideration. This means more upright, neutral and less aerodynamic positioning.
For competitive athletes power positioning and aerodynamics play a key role in fitting. Consider how much time you'll be spending on your bike, what type of competition you'll participate in, and your cycling intensity.
For example: take two hypothetical competitive cyclists, equal in all aspects with the exception that one competes in criterium events and the other in cross-country races.
Comfort would be a primary consideration for the cross-country cyclist, who spends many hours in the saddle, whereas the crit cyclist's power production and aerodynamics are more important for the high speeds and short durations of criteriums. Just as each cycle sport requires a unique bicycle, each sport will have unique fit characteristics.
Riding Style
Competitive athletes must achieve the best fit for their individual riding style and accentuate their strengths. Road racers fall on two opposite sides of the spectrum: climbers and sprinters. A pure climber prefers a level to slightly upward saddle position, shorter stem and wider bars. A sprinter prefers oversize handlebars that are parallel to the ground, a more forward saddle and cleat position, and shorter cranks.
Most road racers will be fitted somewhere in the middle of this spectrum. How you adjust your bicycle for your riding style can be a process of trial and error. Before you move or change a component, carefully mark and measure its previous position and be sure to make only small adjustments. If you're comfortable, but would like to lower your aerodynamic profile, gradually lower your handlebar position over time and allow your body to adjust.
Biomechanics
There's no general formula for the perfect bike because every cyclist is unique. Some are bow-legged or duck-footed. Torso length, leg length, and arm length all vary from person to person, and sometimes vary from left to right on the same person. Backs can be rounded, swayed, or curved, and hips vary in widths. The bottom of the foot may angle inwards or outwards.
It's not always appropriate to adjust your bicycle to compensate for a biomechanical condition, and knowing when and how takes a great deal of expertise. For example, a cyclist who's "ankling" or using the right foot to pedal may be compensating for a left leg discrepancy. This may require special equipment to diagnose the problem and specific shims or spacers to correct it.
If you believe you have a condition that affects your cycling, it's best to find a trained professional who's familiar with biomechanical positioning.
Muscle Imbalances, Inflexibility and Injuries
When you're injured, your body compensates for the injury by using different muscles to do the work of those in the injured area. Even after the injury heals, your muscles may continue to compensate this way, and can cause a variety of problems with pedaling mechanics.
Tight hamstrings can lead to lower back problems on the bike, and cycling in general can lead to muscle imbalances over time. Again, it takes a professional to diagnose and correct these issues. This may mean adjusting your fit to a more neutral position while the area is stretched or strengthened. If you're experiencing an overuse injury, a professional may be able to adjust your fit to alleviate it entirely.
Form
Carefully observing how a cyclists looks on the bike is the best way to determine what needs to be changed. I use a stationary trainer and a video camera for this. I shoot the cyclist from a variety of angles and then play it back in slow motion for both of us to observe. I also use a power meter to help determine if a new position resulted in a loss of power. This type of feedback is invaluable.
Often the cause of discomfort or power loss isn't the fit, but a correctable bad habit. It's important to make this distinction. For example, if the cyclist is complaining of elbow pain and trapezious discomfort it could be caused by using a tight, straight arm versus the slight bend required to absorb road shock, or it could be caused by a stem that's too long.
Getting the Right Fit
Begin by purchasing the right bike for your size. This may mean doing some research on your own or going to a reputable bike shop. Each manufacturer measures frames differently and the frames themselves can vary widely. It's important to know the manufacturer's guidelines for frame size to your height and inseam. That great deal on the used bike you purchased may not seem so great when it's the wrong frame size.
There are a wide variety of fitting systems that use ratios, formulas, algorithms, computer programs, etc. These are even available online, and each with its pros and cons. The most important thing to remember is that every fitting system simply gives you a starting point.
No computer can tell you how your bike should optimally fit because no computer knows your riding style, biomechanics, injury history, etc.. This is where the art of bike fitting begins and it may be trial and error. I use a variety of methods in fitting a cyclist but my favorite tool is a device called a goniometer that measures joint angles.
If you're experiencing joint pain or have an overuse injury, don't wait for it to go away. Get some trained, professional eyes on you. A good bike fitting may cost $100 per hour but it's money well spent if it keeps you on the road pain free or makes you a faster cyclist.