Quite a few things can cause this but probably the most common on an older car is low refrigerant. A low-pressure cutout switch prevents the compressor from running to protect it from damage if refrigerant is too low to carry sufficient lubricant.

Scotty has a nice video on diagnosing and recharging air conditioners in cars. It was the first video he made that I put to real use, and I restored the 21 year old air conditioning system in my Ranger last summer. 

Go rent a set of manifold gauges from your auto parts store and check out Scotty's A/C video to learn how to use them. Check your pressures and compare them against an R-134a pressure chart. If you have no pressure, or it's lower than the chart says at your ambient temperature then there's either a hole somewhere, or it slowly leaked past seals over time. If you have 0 pressure, you can rent a vacuum pump from the auto parts store as well, pull a vacuum, and see if the system will hold one. If it does, you can recharge it. If it doesn't, you can run leak dye through it to find the leak, as long as it's not in the evaporator, behind the dash. Scotty made it very easy to understand, I felt like an expert after fixing mine, haha.