I know this is an old post but the subject is one I'm very familiar with, being a kickboxers and being known to be particularly explosive.

There are two basic ways to improve speed; first, simply try to move faster eg try throwing more punches per minute against a bag (speed bag or heavy bag) second, try moving fast against resistance eg using a moderate to heavy weight push (or pull) as fast and explosively as you can from the start position.
I'll expand on that with a couple of examples.
Time yourself on the heavy bag and try throwing as many punches as you can in 1 minute, each time you do this workout attempt to beat your previous score. Try not to use less range of motion or crappy technique, you'll only be robbing yourself of any benefit if you do that. You won't look like a badass doing this as your technique WILL suffer, no matter how hard you try to maintain it nor will you be hitting as hard as you can, but you will become faster.

Choose an exercise which closely mimics the movement you're trying to improve eg for punches the bench press is good. Choose a moderately heavy weight ie lighter than what you'd use for strength training but still heavy. Lower the bar normally until it touches your chest, pause, then push it up as fast as you possibly can. It won't move fast as it's a heavy weight! However, because you're TRYING to go fast you're telling the muscles they need to go fast so they'll develope to be faster. Remember; just because you're pushing the weight fast on the concentric phase don't start letting it drop down on the eccentric phase. Doing that will increase the likelihood of tearing a muscle or worse.