Whenever I'm doing fight scenes, I try to restrict myself to one or two "action" moves per tag, depending on what the other person has done. For example, the other person tries to hit my character, and I have two moves in response: I either block, dodge, or take the hit, and then respond with an attack. That's one tag. Keeping things simple like that can make the scene easier to follow, AND it means that the other player can choose whether to take the hit or not, which makes things more interesting.

As was said above, loosely work out what the outcome is, and any outcome goals you might have. (ie. "I want it to end in a draw, but let's beat the shit out of each other" or "My character wins, but they lose a hand in the process," things like that.) Communicate with your partner. Don't get too fussy about language, just try to communicate clearly what each move your character does is attempting to accomplish.

Don't control the other character (the above example of "swinging for their jaw" vs "punching them and shattering their jaw instantly"), and don't be that guy that is just so overpowered that they never ever ever get hit, it's boring to play against. But be clear about your character's actual abilities, too. If you've got a fistfight between Goku and, say, Phoenix Wright, there's a serious difference in power levels, there.

And don't be afraid to ask for help or clarification wherever you need it!