There are three important principles of training: Wolff's law, specificity, and recovery.
Wolff's law simply states that the body will adapt to the stresses that are placed upon it.
The law of specificity states that the adaptation to stresses placed on the body are specific to the stress.
Recovery time is needed following the stress to allow the adaptation to occur.
Training is a form of stressing the tissues of the body in a structured manner. In order to go faster, a cyclist needs to generate more power. In order to generate more power a cyclist must train for strength, footspeed, endurance, and increasing of the lactate threshhold.
Strength training is best done in the gym but can be done on the bike, too. I find leg presses to be the best gym exercise. On the bike, overgearing for interval training will have a similar effect.
Cadence training is done with spin sprints.
Endurance training is the goal of longer rides.
Lactate threshhold training is best done in hour-long efforts at time-trial speed.
Create a training program where each of these aspects os focused upon once per week.
Allow time for recovery between training sessions and be sure to weat well and sleep well.
Obviously, this is a very basic outline. I hope it helps a little. Feel free to ask more questions if you'd like help with the formulation of a more structured plan.