I have directed a few successful fight sequences and a few bad ones. There is a lot of pressure on the actors, first of all. Don't try to just "wing it." Firstly, it's dangerous. Secondly, it doesn't film well.
The key for me is to shoot coverage, meaning the I try to film the entire fight--or at least large portions of the fight--from one angle, then again from another, etc. I always include two or three static setups, long shots and medium shots (with minimal camera movement), and at least one time through handheld. As long as the actors have practiced the sequence well enough, then editing the scene will be easy.
In editing of the sequence, I tend to let the shots last a long time. I like seeing actors REALLY fight, so I keep my cuts to the bare essentials.
I've never filmed a boxing scene, though I think that'd be very cool to do.
Is this a real match that you're documenting? Or is it for a fictional story?
Wish I could help you there. I'm not very experienced with lighting. But since it's documentary-style, seems like it should be easier to light. Meaning you have more room for error. =-)
The 2 fight scenes that I shot had multiple fights going on at once. What I did was get a wide shot of all of the fights happening at once. I got a static shot of that for about a minute or so. Then I got a static wide shot of each fight. From there I got static midshotS of each fight for also around a minute, different angles. I went on to get hand held close ups at different angles of each fight for around a minute. I cut them all fairly loose but with enough cuts to keep it moving and interesting. There were about 4 fights that took place in one and 3 in the other. The 4 fights lasted about 3 minutes and the 3 fight sequence was more so a comedy type fight, and had dialogue mixed in. That also lasted around 3 minutes. I used the hand held tight shots sparringly during the editing process. They were mostly used to break up the angles and shot differences between wide and mid shots. For the comedy fight, we let God take care of the lighting, since we were outside in the woods. The other one was at night, on the edge of no where, so we shot under a street light and used car headlights.
You need to do two masters wide or at least wider than tight from each direction and maybe a master from one direction really wide. Then I would move in and go hand held for coverage on both fighters. The best of all possible worlds is that you could double the fighters at least in the wide and for coverage "overs".
Remember that the fight will only be as good as the worst person in the fight.
Is it a boxing fight or street fight?