The vertical jump involves coordinated spine, hip, knee, and ankle extension to produce force in a vertical direction very quickly, while the muscles are shortening through to a very short muscle length. Since the time available for producing force is long compared to other athletic movements, this reduces the importance of rate of force development. Yet, the force-velocity relationship is the primary determinant of the amount of force that can be exerted at a given movement speed. Therefore, maximum force, velocity, and the force-velocity gradient all affect vertical jump height.
My son asked me to get book to help improve his jump and was thrilled with the terrific tips it gave him. According to him, this book covers all the important basics and is a must-read for anyone looking to increase their athletic performance. The exercises are described in a clear, easy to follow manner...and now that I've read it as well I'm happy to say, I understand more of what my son is always going on about! ;)
Learn about plyometrics. Plyometrics are exercises that use the resistance of your own body to build strength and are essential for building the kind of strength necessary to build your jump. It takes time to train your body to jump higher, but working the right muscle groups can improve your explosiveness and height without maxing out regularly in the weight room.
High-Reach Jumps – Are similar to tuck jumps, but instead of brining your knees to your chest, you just reach as high as you can. This is done best under a basketball ring or near a wall so that you can tell how much lower your reach becomes as you fatigue. Try to reach the same height through all repetitions. if you don’t have anything to measure against, that’s fine. Just jump as high as you can each repetition.

The method described above is the most common and simplest way to measure one's vertical jump, but other more scientifically accurate methods have been devised. A pressure pad can be used to measure the time it takes for an athlete to complete a jump, and then using a kinematics equation (h = g × t2/8),[4] the computer can calculate his or her vertical jump based on the time in the air.