If your car's air conditioner isn't working, one of the first things you should check is the compressor clutch. The clutch is what engages the compressor when you turn on the A/C. If it's not engaging, then the compressor can't do its job and your car won't blow cold air. Fortunately, testing the compressor clutch is a pretty easy process that anyone can do.
To test whether or not your compressor clutch is engaging, start by starting your engine and turning on the A/C. Then, open the hood and locate the compressor. You should see a large pulley attached to it. This pulley will be either smooth or grooved. If it's smooth, there will be a belt wrapped around it. If it's grooved, there will be no belt (the grooves are for an internal combustion engine).
Once you've located the pulley, put your hand on it and feel whether or not it's spinning. If it's spinning, then that means the clutch is engaged and working properly. However, if it's not spinning (or if you can't tell), then engage your emergency brake and put your car into second gear (for manual transmissions) or park (