1. Fit: You need to make your bike fit your body–not the other way around. You can usually go to a bike shop for a quick bike fit. They’ll check your seat height, your seat fore\aft position, and your handlebar height. If your bike doesn’t fit you properly, you’ll end up with knee, hip and/or lower back pain–so it’s important to get your bike fit before you start putting in the miles.
2. Fitness: If you’re just cycling for fitness (weight loss, cardiovascular health, etc.), then cycling is pretty straightforward. For the most part, you just need to use your bicycle often. Ride your bike instead of driving your car to the store or to a neighbor’s house. Try to ride more than 20 minutes non-stop at least three or four times per week. Avoid high traffic roads and always wear a helmet.
3. Cardiovascular Health: If you’re a competitive cyclist hoping to improve your performance, the number one thing you can do is to improve your cardiorespiratory endurance. You do this by keeping your heart rate within your aerobic fitness zone (65-85% of your maximum heart rate) most of the time. Your body will become more efficient at pumping blood, you’ll have more red blood cells, you’ll burn more fat, and even your cells will become more efficient at processing energy (because you’ll have more mitochondria). If you prefer, you can purchase a heart rate monitor to allow you to better watch your heart rate while you ride.
4. Performance: If you feel your cardiorespiratory system is developed enough, you can start throwing in some "intervals" (in running they call these fartlek sessions). These are short bouts of higher intensity riding. Just pedal faster for a period lasting between 30 seconds and 5 minutes, then repeat the interval after a short rest. You can vary your intervals by doing some intervals on hills or by using harder gears. Intervals can build leg strength, improve your anaerobic speed, increase your top speed, and even slightly improve your cardiorespiratory health.
I believe I wrote that up in about 10 minutes, so don’t be shocked if you find an editing error in there.