To walk from EPCOT to MGM, you exit the International Gateway between England and France (in the World Showcase).
You follow the canal until you have the option to go straight to the BC/YC or take a left to the Boardwalk. Take a left, which will lead you to the Boardwalk (ESPN Club, Flying Fish, BWV, etc).
Follow this until you leave the Boardwalk and take a left. This pathway/sidewalk will lead you right to MGM (it goes under the road).
Depending on how fast you walk, you can do it in 20-30 minutes (longer if you stop by the ESPN club for a quick one!).
Hope this helps...