There's no separate on/off switch for the compressor. If your A/C isn't working, the problem is likely one of these:
* A/C button: The simplest possibility is the button on the dash is malfunctioning.
* Relay: The relay that powers the compressor may have failed. This is a common point of failure.
* Low refrigerant: The system might be low on refrigerant, requiring a recharge.
* Compressor clutch: The compressor's clutch might be seized or worn out.
* Other components: There are many other potential problems within the A/C system itself (pressure switch, condenser, evaporator, etc.).
To troubleshoot, you'll want to check the relay (which is often located in a fuse box under the hood or dashboard) and then consider taking it to a mechanic familiar with automotive A/C systems for proper diagnosis. They have the tools to diagnose low refrigerant and test the electrical components of the system.