When doing training for the sport of cycling there are some specific things you need to focus on.
First you are going to need very strong quad muscles for the activity of cycling in order to generate power. If you happen to be cycling uphill you are particularly going to call this muscle into play and cycling itself can actually be one of the best strength training exercises around for the quad.
The second reason you need to have strong quads is because it will help with knee injury prevention. When you are moving constantly in this motion there is a lot of wear and tear on the knee cartilage and tendons. Additionally, if you do not have a strong quad, the kneecap may start moving irregularly which also will create pain.
Some great exercises to do to strengthen the quad are squats, lunges and leg extensions. You should take note though that if you are already experiencing some knee pain leg extensions may not be the best exercise for you as this does create a great deal of stress on the knee cap as well.
Other options for you as well are wall sits, where you move into a 'sitting' position while keeping your back against the wall, squat jumps (this will help your explosive power) and the leg press exercise. Performing two or three of these exercises each leg workout you do in the gym will go a long way towards strengthening this muscle and enhancing your performance.
Also be sure to always perform a proper warm-up before partaking in this activity as well as some good quad stretches so they are loose and can move through the entire range of movement.
By making sure you include these aspects in your training program you can be sure to enjoy this activity and remain injury free.