When leaving the Magic Kingdom you take the Express Monorail to the Transportation & Ticket Center, then you walk over to the Epcot Monorail. In total I would say it could take at least 20 - 25 minutes, however if the Epcot Monorail is already at the TTC then it will save you a couple of minutes since it takes a while to arrive from Epcot when it's not there.