Okay, having shot numerous live shows I can tell you that the best way,
period is to convince the bands to invest in renting a digital board that can output full mixes...
Okay, hey, I know this is the real world; I've only been that lucky once and that was a venue-thing. Ralck's right about setting up in the back, definitely a good idea. If you've got a few good mics and the space then throw out a fair selection of 'em. If you've got access to a field mixer run them through that rather than your camera and sync the sound in post.
If you come off the house board then plead with them for a separate aux send. Try to get one that's pre-fader and during sound check stand there with a pair of headphones and get it balanced to your liking. The key about doing this is arranging
way before hand with whoever's running FOH. Having run FOH countless times I can tell you that the last thing I want to have to deal with is some photo or camera guy coming up to me saying 'can I plug into your board?'
Figure out what board they're using before hand, determine all the various ways of coming off the board, and have cabling solutions and a sales pitch prepared for every one of them. Don't expect to get a great mix though, no matter what you do... Mixing sound for an audience and expecting it to sound good on tape rarely turns out more than, 'okay'.
And even if you
do pull a feed off the board... set a microphone or two up also as a back up. It very well might just sound better.
I say this because when you're mixing a live show generally the guitar amps onstage are providing alot of the sound for the guitars and you really only flesh out the guitars in the mix, whereas the vocals and drums tend to end up overpowering in the mix, leaving you with an audio track that sounds
incredibly weak. And isn't fixable.
Hope this helps...