I dislocated my pinky finger and popped it back into place last week, how long will it usually take to heal?

Depends: It depends on the amount and nature of injury you had. If there's no fracture, i'd recommend buddy taping or having it in a finger splint for as long as the pain subsides and then you start doing some range of motion exercises until you are able to fully use it. If there's a fracture, the finger must be buddy taped for a number of weeks (depending on the fracture) and then as above.

Quickly: It should heal quickly unless you have a fracture. There is no way to tell for sure without an xray. For treatment, taping to the ring finger will help speed recovery.