How does automotive HVAC work?

Basically the same as your home air conditioner with the exception that the compressor is driven by the motor of the car instead of an electric motor.

All vapor compression refrigeration systems operate by using a refrigerant to move heat from the space you want to cool (inside the car) to the place you want to reject it (the great outdoors).  The refrigerant starts as a warm liquid as it leaves the condenser.  This warm liquid will be about 10F warmer than the outside air temperature.  It then goes through an expansion device that drops the pressure of the refrigerant.  Dropping the pressure reduces the boiling temperature down to a temperature at least 10F colder than the temperature you want the air to be that is blowing into the car.  This cold refrigerant goes through the evaporator coil where it evaporaters...or boils...at the low temperature.  As it evaporates, it absorbs heat from the air stream and turns completely into a vapor.  This vapor travels on to the compressor where it is compressed from a low pressure to a high pressure.  The new high pressure imparts a much higher boiling/condensing temperature.  This temperature is high enough that when the vapor goes into the condenser, it can reject heat to the great outdoors and condense into a liquid.  Now the process begins all over again.