Great question, Sweeper.
I train for power when I lift weights. F=MA and typically maximum power (F) is attainable at around 75% of your one rep max (M) and, by nature, at maximum voluntary speed (A) of the contraction.
So, say your 1RM is 250 pounds in the close grip bench (a lift I often use because it most closely resembles puching). Typically, you will generate the maximum 'F' (aka power) in the equation with 'M' equal to 185 pounds and 'A' dependant on training, will, mood and the alignment of saturn and the constellation Orion (<-- joking, but it's all mental which is to say, unpredictable).
To get maximum acceleration (A), nervous adaptation must be worked for a period of time using this type of training. It does not come naturally, though some people are more gifted in this area than others. As with all other things, start slowly and build in both intensity and speed.
All of the caveats surrounding plyometric training apply here as well; a little goes a long way and a lot can lead to stress injuries or more gross failures. Never allow the bones to "lock" at the top of the movement, always stop the weight sharply before (like the focus in a punch). Be VERY careful exploding from the bottom of the movement where your joints are typically compromised -- instead feel like a bottle rocket that accelerates very quickly but smoothly and doesn't "jerk" out of the hole. Rack the weight when you can no longer rattle it at the top of the movement.
After a bit of light practice you should be able to begin to add weight. Just don't add the full juice until your body is very used to it. Like plyometrics or heavy squats, once a week is plenty until it's second nature, and don't go over twice a week regardless of how confident you feel. This training is more dangerous than some types, but not any more so than doing singles or doubles on a regular basis.
Lifts to use this balistic training with might include: close grip bench, push press (a "cheater" military press), squats (carefully!), and of course the power lifts like cleans and power high pulls.
Technique and mental state are still top dogs, as far as I'm concerned. But balistic training will do wonders for focus, speed, concentration, explosiveness, connective tissue density, and, of course, power. WIth me the results really blew my mind. I broke through a long held plateau in my 1RM bench and techniques like the no-inch punch were much more satisfying to practice. All competent strength athletes cycle through this type of power training regularly. It's not well used by other people (and especially not the Muscle and Fitness gym experts), but it's well understood and very effective.
There are many many more points but I'll leave it at this. Hopefully some others will chime in as well and hopefully this won't get moved to some other category that gets about 2 hits a month (happened to me before... very frustrating). Great thread.
Travis Roy
www.jrroy.com