Fitness
There are basically three ways to get stronger on a bicycle. You can increase endurance by riding farther, increase speed by going faster and increase power by climbing hills, headwinds and heavy loads.
Endurance
The secret to being able to ride farther? Ride a little farther each time. On this type of ride, concentrate on smooth, easy pedaling over flat terrain. During bad weather days, you can increase your indurance by doing your cardio indoors using an stationary bike.
Speed
Interval training (in which you work out at near-maximum effort for a set period of time, then recover for another set distance or time, and repeat the whole thing a specific number of times) is a basic concept of aerobic exercise that is perfect for advanced and beginner cycling as well. It doesn't have to be anything complex: Pedal all-out for 20 or 30 seconds, slow down for another 20 or 30 seconds, then do it four more times.
Power
Building power means building muscle as well. Consider a cyclist weight training program to gain muscle mass. When riding, use a lower gear than you normally would, or look for a hilly stretch of road to ride on.