...and following on from Ransoman, the pulley at front of compressor has a separate disc clutch at the front of the pulley, which as he correctly said, does not spin when compressor is off. When clutch is engaged, the pulley (which freewheels when compressor is not engaged) and clutch lock together, and internally, the workings of the compressor begin to rotate and move refrigerant around the AC system. With 12VDC applied to the compressor clutch wire (while engine is running), the clutch should engage. If not, the clutch is either shot, or the compressor has siezed. If it was working before, and just gradually produced warmer air at the vents, it could simply be that the system has leaked gas, and the low pressure switch in the system says 'don't run' to avoid compressor damage. The system has many pipe and hose combinations, and the hoses typically develop leaks, either along their lengths, or at the crimps where they join pipe. Or the coils (condenser at front of car, evaporator at firewall) have developed a pinhole leak which allowed gas to escape. Most likely causes. Compressors are pretty tough (my company makes them, globally...) and take a lot of abuse.
A Kwik Fit or similar should have a set of gauges they can put on high and low side of system, to determine if there is gas pressure in the system. Shouldn't cost much to diagnose.
Take care when using the hot wire technique on the compressor clutch, lots of spinning parts up there, make sure you stay clear of the clutch, and other rotating items, while doing the diagnosis...