Mac is spot on with all of his recommendations.

I will expound on his response just a wee bit. It's possible that if you get a mixing board with the PA system, that it may not have clipping lights for each channel. If not, there is a good chance that there may be PFL or Pre-Fade Listen buttons for each of the input channels.

When these are depressed, on most boards, the VU meters for the board will be switched over to meter those channels that are PFL-enabled, rather than the mains of the board.

This just turns the VU meters into a fancy clipping meter. I recommend a few steps when I encounter a new board I haven't touched before.

Step 1. 'Zero' the board. Sometimes, this is as simple as taking the edge of your index finger, starting at the highest input channel, and running it from right to left across all of the input trim controls so they go to their extreme counter clockwise directions. If you can't do that easily, just go through and turn all the trims manually to their zero settings. Some boards have a switch for mic vs. line level. Make sure to get those switches set properly first as well. Second part of zero'ing the board is to put all of the aux channel settings for each input channel strip to zero. Last step to zero the board is to put the channel EQ settings at their neutral positions (usually straight up and down). Most boards and setups sound pretty doggoned nice at their neutral settings for line level inputs (like program material on CD, keyboard outputs, etc.) if you get the mains EQ'ed properly for the room(detailed below).

Step 1a. If the board has a high-pass filter setting for each channel, where the corner frequency is at 80-120 Hz or so (sometimes written right on the board itself, always in the manual if there), then enable that thing for every single channel except any bass guitar or kick drum. There is absolutely no need to have that frequency content in any signal except your lowest end instruments. Enabling it will help to eliminate unnecessary rumble that can occur from bumping into mic stands and what not. This is also very good practice for recording. Always, always, always put in high pass filtering if possible, on most mic'ed and line-in channels if you really don't need the low end (again, generally true for everything except bass instruments and kick drums). This can clean up a muddy mix tremendously.

Step 2. Set the trim control for each input channel and the main output as per Mac's instructions, or if you have PFL, enable it one channel at a time and use the VU meters, letting the max hit in the yellow region of the VU meter (most are color coded green-yellow-red).

Step 3. EQ the main output/speakers. Good practice to bring along some music you know well on CD in CD format and put it into the board's tape-in connections. Run that to the output and set the EQ for the main speakers either on the board (if there is a main EQ section - many smaller boards have a little 7-10 band EQ for this) or in the outboard EQ that should be after the output of the board and before the amp for the speakers.

Step 4. From here, usually my next step is to set monitor levels and EQ, but often times, this isn't available or even necessary for smaller venues and setups.

Lots of further steps, but following these, can help you to get the basic signal gain staging set properly for mixing on a board. If you get reasonably good at even these steps, you will be considered a hero by many. It's amazing how many folks don't get these pretty basic steps and end up with a feedback-prone, terribly EQ'ed setup.

Other tricks of the trade for live sound:

1. Know your formant frequencies. Forming these vowel sounds with your lips while exhaling/whispering can help you pinpoint at least octave band issues.
'ooooo' = 250-500Hz, 'aaaaaahhhhhh' = 1000 Hz, 'anh', voiced as the nasal 'a' sound in the American English pronouned 'bank', 'cat', 'flag', etc. = 2000Hz, 'eeeee'=4000Hz.

If you feel silly doing this, then another way to learn these is to find a graphic EQ and put your favorite music through it - first setting the EQ flat to zero, then one at a time, raising a slider all the way up, and all the way down (easier to hear peaks than it is a lack of content). Do it several times, with several types of music - but best to do it with the kind of music you'll be mixing. If you practice this for even an hour and make some mental notes, you are well on the way to learning to hear 'peaks and valleys', but likely 'peaks' easier.

2. Don't use speaker monitors if you can avoid it. Hey if the singers and instrumentalists are keeping time and relatively balanced - kill the floor wedges and hot spots. On-stage volumes are the bane of running a good mix. If you have to have these in place, it doesn't hurt to bring the levels down gradually if there are no complaints and no detriment to the mix.

I've got more, but I see I've typed way too much.

-Scott