Hi there, Carrie!
There are a couple of ways to get to the
Downtown Disney Area entertainment district from
Epcot.
1. Head towards the International Gateway in Epcot's World Showcase. This exit is between the France and United Kingdom pavilions and offers walking access from Epcot to Disney's Yacht Club. Disney's Beach Club, and from Disney's BoardWalk Inn. At any of those Resorts, you can hop on a bus that will take you directly to Downtown Disney.
Bear in mind, though, that the Epcot bus to Downtown Disney might make stops at several of the Epcot-area Resorts, including each of the ones mentioned above. You'll definitely want to build in time for that contingency.
2. At the main entrance of Epcot, catch a bus to either of Disney's Port Orleans Resorts. From either Port Orleans, you can then take a leisurely boat ride along the Sassagoula River.
3. Again, head to the main entrance of Epcot. Catch any Resort bus. When you arrive at the Resort, change buses to a Downtown Disney bus.
Finally, there's the quickest and most direct way: Taxi. You'll find a number of waiting cabs at the entrance to every theme Park, and for a fee, can be taken directly to your destination.
Have a wonderful time!
See you later, celebrator,
-Deborah B.