I've never been in a serious fight, but here are a few things that might (hopefully) help you:
The best way (debatably) to punch some one is to start with your hand curled into a fist, fingers up, with your arm bent so your fist is at your side. As you bring your arm forward, untwist it so your fingers face down.
In a real fight, the object is not to look stylish (in a script this might be different). The object is to cause the other person as much pain as possible. Hair pulling, biting, clawing etc. are all used.
I can't think of anything else right now. . . Hope this helps a little.
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