What and How long does it take to actually "buy" a used car? (Dealership)?

A lot of it depends on what you are trying to do. Do you have a trade or are you buying straight out, no trade, are you paying cash or do you want them to get bank financing for you? The car should be pretty much ready to go unless you ask for some extra things to be checked out or done to the car. If you're paying cash you'll only need to sign a couple of forms for the dealer and then what ever is required by the state. If you're financing You'll have to wait for the banks approval and sign the same form as cash plus the banks contract and agreement.