Get familiar with your hardware. Compressors vary so you need to know what your specific model includes. The basic adjustment most all compressors have are threshold, attack, release, ratio and output (or makeup) gain. You may have other buttons that will automatically control the attack and release. You also may have multiple channels on one compressor.
Set your threshold. The threshold determines the level the signal must surpass for the compressor to start working. This is the parameter you will have to fine tune the most. Once you have signal going to your compressor, watch your meters and adjust the threshold until you have the desired amount of compression. Typically, you only want the gain reduction to be a few dBs but you may press it harder for certain applications.
Dial in your attack and release. Attack is how long it takes for your compressor to start working once the signal has surpassed the threshold, measured in milliseconds. Release is how long it takes the compressor to stop compressing once the signal falls below the threshold, measured in seconds. Setting these parameters takes a fine balance to get natural sounding compression. A good place to start is a 5ms attack and a 1 second release, and from there you can fine tune.
Decide how much the signal will be compressed with the ratio. A 2/1 ration, for example, will compress the signal 1dB for every 2dB it exceeds the threshold. A higher ratio like 10/1 or 20/1 is more limiting than compression. A ratio of 2/1 is a good place to start and in most general PA situations, you will not need to go over 3/1 or 4/1.
Make up level with the output gain. Often you will find that your dynamic level is closer to where you want but your overall level is too low. You need to use your output gain on the compressor instead of your preamp gain or channel strip fader. If you change the gain on the mixer, you will be sending more signal to the compressor but the output of the compressor won't necessarily be louder. Turn up the output gain to keep the correct balance and sound.