A basic PA setup will consist of microphones, instruments or other sound sources connected to a powered mixing board (i.e., one with its own built-in power amplifier). It's also common for PA systems to use separate power amplifiers, and the most complex systems include additional components that may amplify the signal level (a "gain stage"), including equalizers, crossovers, compressors and other signal processors. After going through all of the gain stages, the sound passes through the PA's speakers. Each step in the audio chain introduces a potential for distortion.
The most basic and important step is to start with the simplest audio path and the lowest levels. Mute individual channels on the mixer to see if distortion is happening "across the board" or only with a single channel. Turn down all of your volume and gain controls and bring them up in small increments -- this includes frequency bands on mixers, equalizers and crossovers, which may be boosting a single frequency range far beyond the level of the others. If you can isolate the source of the distorting signal, preventing distortion is a simple matter of turning it down so that a clean signal is sent to the next stage.
Preventing distortion may also be as simple as changing the mike positioning. Placing a microphone farther from the source will decrease the amount of sound that goes into the mixing board. This is especially likely if you are getting distortion mainly in the bass frequencies, due to a phenomenon known as the "proximity effect." If the microphone or any other sound source has a preamplifier between it and the mixer, make sure that the gain control can be set to a level that isn't overdriving the mixer channel.
Amplifiers and speakers must be properly matched to avoid clipping and equipment damage. The important specifications to check are the impedance rating (measured in ohms) and the power handling (measured in watts). As a general rule, the impedance ratings should match and the amplifier's continuous power should be two to four times the individual speaker's continuous power handling. "Peak power" is very different from continuous power, and represents the extreme limits of the speaker's specifications. If you are experiencing consistent distortion, you may be driving your speakers with too powerful of an amplifier.
If you've exhausted all of the gain options and made sure that the equipment is matched properly, your distortion may be the result of failing equipment. This could be anything from physical damage, such as torn speaker cones or bad wiring in the cables, to malfunctioning components on the circuit boards of the electronic equipment. Electrical interference can cause distortion, entering the audio path through unshielded wiring or the receivers of wireless equipment. Remove as many elements from your PA system as possible to try to isolate the problem, and repair or replace as needed.