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.