How does the air conditioner in your car work?

The answer's a bit more complex, but, in a nutshell...

As it moves through the compressor, the refrigerant is pressurized and becomes heated. This heat is acquired through pressure, and also from drawing heat out of the vehicle's passenger compartment. As the refrigerant moves to the condenser, it is considerably hotter than the ambient air which is flowing through the condenser fins. The most basic law of thermodynamics is that heat flows from a warmer object to a cooler object - thus, the heat is transferred from the refrigerant to the air passing through the condenser fins (a car's radiator works in the same fashion), which causes rapid cooling of the refrigerant. Fast forward through the metering device, and to the condenser, which has two functions - it exchanges heat and moisture from the passenger compartment to the outside air, and it also channels cold refrigerant through the HVAC compartment (which contains the heater core and blower fan, as well). The blower fan blows air over the evaporator, and into the air conditioning ducts, delivering cool air into the passenger compartment.

That's the simplified version.