Not how to set-things up, this bit assumes you know what things do in terms of how to plug everything together, but comments on how to bring it all together in the mega-stressful, huge-fun environment that is the live show.

There are no hard and fast rules, but like any art, there are techniques generally regarded as the best method of doing things. When starting a mix, start by establishing a rough basis of the drum kit and bass sources. If the vocalist's there, do vocals next, because you will be balancing the backline and rhythm to the vocal level, not the other way round. Otherwise, get some relative levels in a sub-mix (group) and adjust the group level later. 
Piano and lead (ie: rhythm section) brought in, followed by whatever else is needed. If it all sounds too complicated, or "busy", even after panning, try EQ-ing overlapping sources to thin them out. Despite sounding very strange in isolation, when sitting in the mix can often do the job.


The positions of the stereo pans was probably the last thing I learnt how to do effectively. More important for recording, but then you have time enough to re-play the mulitrack, panning is important for live use to unclutter the sound, add depth to the soundscape and simply to take some load off the amps and cabs in the sound system. When done properly, makes a large difference to 'listenablilty' and drawing the audience into the performance.
Obviously, anything significantly bass needs to be firmly centre, to make best use of the cabs, as do the lead 'timing' cues, like snare, hi-hat or any drum synths.
Vocals - The lead vocalist will generally also be dead centre, as that's where they usually are on stage. Backing vocals are often positioned to one side (~80%), but if many feeds are used from backing, some like to pan different mics to different sides, to pan different lines/voices. Keyboards, lead, purcussion and other backing are generally distributed in varying 'positions' around the vocalists; according to what's right.....
....add effects last (except drumkit gates).


The process of finding the frequencies where feedback will occur first, killing them, so the overall gain can be higher. Most important on the monitor network, because those speakers are pointing straight at the performers, therefore the mics.
Method is simple, flat the EQ, increase gain until feedback starts, just below this level it 'rings' when someone talks into the mic. Identify the frequency of this ring, cut the level by half on the EQ (ie: a 3dB cut), increase the gain once more until more ringing occurs, repeat the process. If it's just the same again, continue cutting. The process normally identifies four or five frequencies where feedbak is a significant problem, but, in theory could continue forever, until you have every freq. at maximum cut. 


Remember to kill this for announcements between songs and watch-out for the band talking to each other if mic'd up.

EQ'ing the Entire Mix - Only really done in live situations can can be vital. The reason is to correct the tonal differences of the room&PA combination, so the "perfect" sound fed from your desk output will still sound perfect. With the lack of pink noise generator and Specky-analyser, the only real way to do this is to soundcheck to a recording you know well and adjust accordingly. BUT, it's not quite that simple; once the audience is in place, many variables, like the humidity and temperature of the air in the room, absorption ratio of the people themselves etc. etc. shapes the sound still further. As a rule of thumb, the spectrum will tail-off above around 6-8kHz and needs boosting slightly in these frequencies. This is why the soundcheck in big concerts (esp. enclosed rooms/halls) always sounds excessively bright, but fine "on the night"; the well-experienced engineer meant it that way.

Compressing the Entire Mix - Because compression reduces the dynamic range, on one hand, compression of the entire output can result in the sound actually appearing quieter, as there is no-longer a 'contrast' present.
A much more effecive reason to compress the entire mix in a live situation is to avoid excessive, square-waving peaks accidentally reaching the main PA. The mix is kept around 0dB, but compression set to threshold at this level, with a fairly high ratio (1:5 - 1:7), so, if any signals higher than 0dB do "slip though" the compressor catches them and rounds-off the squarewave. Quite often you'll see the lights on the compressor flash on and off briefly and think "Why are we bothering?" It's exactly this, that after a 3 hour performance, that can make the difference between cooked amps, fried voicecoils and a not-shagged PA.
HAVING SAID THAT, the compression details above will sound shite if you're trying to process an entire mix for recording reasons. The situation above is a 'safety net' and, ideally would never be needed.