To see if the compressor is engaging, simply look at it with the engine running while someone turns on the a/c with engine running. The very forward portion in front of the pulley will not be turning with a/c off. When a/c is turned on it should turn.
If it is turning, see if the blower is running. If the blower is not running, you need to troubleshoot the blower. If it is blowing HOT air all the time, and I mean HOT, not just not cool air, then the heater valve is being turned on and you will need to troubleshoot the ACC to see why the heater valve is on all the time.
Hope this helps,