Once you exit MGM, if you go towards the left (lake) you can catch a boat. The boat will stop at the EPCOT resorts (Swan/Dolphin, YC/BC, and Boardwalk) and then continue to the International Gateway of EPCOT.
If you would like to walk, you also hard to the left and follow the sidewalk past the parking lot that follows the lake/river. This will bring you past the EPCOT resorts. I would guess it would take about 20 minutes to walk it (if you don't stop for a beer on the Boardwalk). It should be noted that you can sometimes get to EPCOT faster by walking then taking the boat.
If you take a bus, you might have to go to the TTC or Downtown Disney. I have never done this and I am not sure there is a direct bus to EPCOT from MGM.
Hope this helps!