I'm going to assume you paid by credit card and haven't printed your tickets. If this is the case, almost always it is pretty instantaneous. However, the credit card company can hold onto those funds for a few days so while Amtrak has credited your card it might not show up right away. Also, there was one time where I had to cancel a trip and it took about 4 days for them to issue the refund. The agent said that over 40 changes had been made to the itinerary (not sure how that happened), and it would have to go through the refunds department where they would have to reverse all those changes before the system would allow credit back.