Without the year, make or model it could be any of the following..
1. Relay.
2. Sensors.
3. Clutch hub worn out.
4. A/C - heater controller.
5. PCM or ECM bad.
It would be best to scan the vehicles computer so that you can find out just what is wrong......
most likely it is out of freon
Turn the compressor off.
A lot of vehicles will activate the A/C compressor in 'Defrost' mode. Either Bi-Level or defroster will turn on the A/C compressor. I know in a lot of GM vehicles, even just the floor selection will turn it on.
For residential equipment it is 24 volts
You may need to replace the heater\ac control switch, it may be stuck in the off position which would prevent the blower and the ac compressor from turning on.
Check the Freon pressure first. The AC compressor will not turn on if the Freon pressure is too low.
Do you mean that the AC clutch does not engage the compressor? Or do you mean that the AC compressor won't turn even if the clutch is engaged? If the compressor is siezed and will not turn even if the clutch is engaged, the only choice is to replace the compressor. If you can turn the compressor by hand (understand that the belt pulley will turn freely with the engine if the clutch isn't engaged) but the compressor clutch isn't engaging, it might just be out of refrigerant. There is a sensor, usually somewhere near the receiver/dryer) that detects the "low side" refrigerant pressure. Once the refrigerant pressure at the sensor drops below a specified level, the compressor will not turn on. In other words, if the compressor clutch won't engage it might just be out of refrigerant.
The ac compressorThe ac compressor
the ac belt or the compressor bearings are going bad
the clutch on your A/C compressor needs to be replaced.
IT should turn freely when the a/c is not turned on.
If your car has a Serpentine belt that's one piece and made specifically for that engine, chances are you may have to repair the AC unit. From the description "snapping belts" one would assume that the AC Compressor is siezed, where the pulley doesn't even turn freely.