The cold gas from the expansion valve flows directly into and through the evaporator tubing. Guess what? The evaporator is just another heat exchanger. In the heat exchanger called the evaporator, the cold gas flows through the tubing and the warmer air that needs "conditioning" is pulled through the fins that surround the tubing. You and I like to say that the coldness of the pipes and fins cools the air that flows over the fins. Thermodymics people like to say that the heat is removed from the air flowing over the fins and transferred to the gas in the tubing; the heat is then carried away by the piping, back to the compressor. No matter how you look at it, the temperature of the air flowing over the fins falls and the temperature of the gas in the tubing rises. The "conditioned" air is blown into the car’s interior and the (somewhat) warmed gas is returned to the compressor, where it is recompressed to start the cycle over. The return pipe to the compressor is actually pretty cold in operation, but it’s warmer than the gas inside the evaporator.
The evaporator is under the filter/dryer, out of sight, in a housing that joins to the cabin blower motor (in the aquarium).