Keeping it simple:
With the ACM, hot bleed air from the engines is piped through usually 2 heat exchangers (cooled by RAM air). Then it goes into a Compressor where it is compressed to a high temperature. Then goes through another heat exchanger where it cooled slightly. Then goes through an expansion turbine (connected to the compressor) where the process of expansion will greatly reduce it's temperature. It's now cool enough to go into a mixing box, where it is mixed with either hot bleed air or recirculated cabin air so that it is the correct temperature for going into the cabin.
The type of Q's you might be asked would be:
Where does the air come from for the Air Conditioning ?
How does it cool the air ?
At what point do you think the air is the coolest ?
Freon is slightly different. I don't know on what aircraft they use Freon machines but i thought some smaller turbo props might have them.
A Gas (Freon) is compressed into a pipe, it's temperature increases (as does the pipe), the gas is now allowed to expand where it's temperature drops (as does the pipe). Air that needs to be cooled is blown over the cooled pipe (as a result of the expanding gas inside). The fridge in your kitchen works like this.