Training "speed" in the upper body.
Here are two great exercises for training speed (e.g. for pushing, throwing, punching) in the upper body. They are fairly adavnced exercises and there are easier variations which I describe later.
First is the plyometric pushup. Of course you should be pressing a decent amount of weight and have the core strength to so pushups easily (40 or more in a row probably...) Arrange some stuff higher that the ground level so that you can drop in between. Push off hard (A and B) and land inbetween catching yourself in the bottom position (C not shown sorry!) then from there, immedieately EXPLODE up and end up back on the blocks (D). Start with lower blocks. Work up to higher stuff!
A
Second is the drop pushup, its a "shock" exercise that teaches the body to decelerate effectively from upper body loads this is awesome for injury prevention. Its especially useful for athletes who have to break falls, impact opponents and crash into stuff (or people) in general. Start with arms extended (A), then just let yourself fall(B) and catch yourself in a pushup bottom position(C). If you cannot do this (and its a tough one!) you can try this from a kneeling position first before moving on to a standing drop.
The progression is as follows:
1. From kneeling position
2. From kneeling position with partner pushing you from behind
3. From Standng position
A