Usually it has to do with low refrigerant pressure. If there's not enough refrigerant in the system, it won't turn the compressor on to prevent damage. That or the clutch is gapped too wide. Just whack the clutch face with a broomstick while in MAX A/C to see if it turns on. If it does, you need to re-shim the clutch.
The easy way to test for low pressure is to find the Accumulator/dryer. It's a black thermos-looking thing on the passenger side firewall with two large refrigerant lines coming off of it. One of them has the low side port, so it's within 6 inches of that.
There is a fairly large plug on top of it. This is the A/C Clutch Cycling switch - it measures pressure in the system, and if there's less than about 25psi, it opens the switch, preventing the compressor from turning on.
What you need to do is unplug that connector, and stick a paper clip in the vehicle side of the plug. This shorts that switch on and makes the car think there's plenty of pressure. Then put it on MAX A/C and see if the compressor turns on. If it does, you need to put more refrigerant in the system.
If it still doesn't turn on, whack the clutch face with a broom handle. If it turns on then, you're low on refrigerant and you need to re-shim your clutch.
If it still doesn't turn on, then with the cycling switch shorted, unplug the connector to the compressor field coil (right behind the pulley) and check for +12V with a multimeter. If you're not getting it, something is wrong either with the wiring, or with the CCRM, which sends the signal to the field coil. If you are getting it, the field coil is burnt out (this is rare).
