I'm sure Bill will go into more detail with this but I'll add my two cents for the sake of immediacy.
I'll use the bench press for an example.
Your pectoral muscles are the ones that are contracting, doing the work. Do they do work only when you push up? I hope not, otherwise you are just letting the bar drop when you move it back down to your chest. So here is how it works.
Concentric action: Pushing the bar up, your pecs are working as they shorten.
Eccentric action: Letting the bar down in a controlled manner, your pecs are working while lengthening.
Isometric action: This would occur if you just held the bar still, but is done best when you do a typical squeezing your hands together at chest level. Your muscles are working, but they are staying still.
Concentric contraction has the most applications in everyday activities, as you will see in our striking.
Your muscles, however, are strongest on eccentric movement. This is where negative lifting comes in play. Back to the bench press, a weight that is above your max is placed on the bar and you slowly let it down. Your spotter(s) help you lift the bar back up and then you let it down again slowly. Though this gives you a chance to work with higher weight than normal and is considered by some to be helpful at increasing your maximum lift, it is difficult to
directly apply eccentric contraction to many everyday situations.
Isometric work is actually, I believe, seen more in Uechi-like martial arts than in the majority of sports. Consider Sanchin kata. Practicing staying in your stance without moving is an isometric movement. Even when movement is performed, enough of the body stays still that those parts are still working isometrically.
However, isometric practice only increases the strength of the muscle at one position. So, as far as movement is concerned, why would an all-out isometric contraction benefit you any more than an all-out concentric or eccentric contraction? Consider:
Only one or two seconds are required to take a curl from thigh level to chin height. The hardest part of the curl is not the start or the finish, but instead the middle of the curl, where leverage causes the greatest effort. Yet the muscles are in this position for only a fraction of a second. With isometric contraction, the muscles would be exerting full force in this position for twelve seconds, so, theoretically, one effort here could build as much strength as more than a dozen repetitions performed in the conventional fashion.
--Little, John. Bruce Lee, The Art of Expressing the Human Body. p. 36
If isometrics are used to strengthen the muscle at the location where it has the least mechanical advantage in a specific movement, it increases the overall load that the muscle can bear over a full range of motion.
Now, dynamic tension. This is interesting, because you are working one muscle concentrically when you are moving the other muscle eccentrically. An example: lets look at your biceps and triceps as you straighten your arm. Your tricep is shortening, going through a concentric contraction. But your bicep is lengthening, going through an eccentric contraction. Both muscle groups are doing the work against each other. Then you start to bend your arm. Suddenly, your biceps are going through the concentric contraction while your triceps are going through the eccentric contraction. But they are both still working. You are providing resistance for each muscle group from the other group. Talk about multitasking. However, dynamic tension would not be directly applied in an altercation. You would not want one muscle group slowing your motion when the other group wants to strike. Otherwise you'd eat up a lot of the power you can generate. However, dynamic tension can be great at training your muscles to fire with maximum power during the entire range of a striking motion.
Is any one the best way to go? I don't think so. I work my muscles in all three ways. Explosive motion is almost entirely a concentric movement, but isometric action is clearly a part of our system also, and both isometric and eccentric work can be done to maximize our concentric abilities.
I may be totally off on some of this but if I am I'm sure somebody will tell me.