what type of exercise would one have to do to improve his/her jumping height?
jumping is similar to sprinting in that to improve it you need to do it.
start incorporating all types of plyo-metric box jumps into your routine.
as far as weight lifting exercises: jumping is an explosive movement that requires power and is generated from the qlutes, core, hamstrings, quads in a coordinated effort. exercises that work just that are cleans, hang cleans, dead lifts, squats, overhead squats etc.
There are so many to name!
All variations of deadlifts and squats help. Core work is important. If you have access to a ghr. If your strength is sufficient, plyometrics help and last but not least, jump alot.
Keeping your bodyfat low helps as well.
When I was trying to increase my jumping ability I did very well with using box jumps and working my way into the low 50 inch range. Also, where ever I would go I would size things up and think to myself…could I jump over that. Then try it.
Research everything and try lots of things. Train SMART and healthy. Good luck.
Here’s a good website
Yes, the big lifts with big weights help a lot and if you’ve ever seen any Olympic lifters jump after a sucessful lift it could lead one to think about incorporating some cleans and snatches (power or hang versions would be just fine).
squats and depth jumps
I would recommend Deadlifting first and foremost. Squatting is ok, but people squat differently, and some are very quad dominant. You are not going to develop the power to fly through your quads, your just going to end up looking like a fat fuck trying to jump for a meatball. To jump you have to have a posterior chain. End of story. If you can definitely get your posterior chain into your squats then they can be used, but I would still rely heavily on deadlifts. After this I would not waste anytime beginning to learn cleans and snatches, they teach the body to work as one fluid unit by incorporating every muscle into upward force. Even the upper body has a role in jumping and this will be trained olympic lifting…
Think of it as a lower body shot-put. Basically you’re just throwing your body into the air. Actually the body offers more resistance to a jumper than the shot-put does to a thrower…do 100 benches with 15 pounds in each hand…then 100 half squats…which one is harder?
But anyway, obviously good shotputters have good strength…so do good vertical jumpers.
If the ability to create tension is there, all that’s left to do is hone th efficiency of the movement and the rate at which tension can be manifested, either of which can be perfected by practicing the actual movement skill and/or dropping body-fat.
So short answer. Get strong and practice jumping. 
Exactly, kelly.
Very well said.