There is direct transportation between all Disney theme parks. From outside the Epcot entrance, you can take a direct bus to Disney's Hollywood Studios or Disney's Animal Kingdom. To reach Magic Kingdom, you will take the monorail to the Transportation and Ticket Center. There, you will switch to a different monorail (or take the ferry) to reach the main entrance. In the event any monorail is out of service, Disney will provide buses.
At Epcot, the area where off-site shuttle buses load/unload is right next to Disney buses. The monorail station is slightly further. Just look for signs that tell you which bus bay to enter to reach your destination. If you have questions, there's usually a Disney Cast Member around.
A: Epcot Main Entrance
B: Monorail Station (outside Epcot - no admission required to use)
C: Parking Lot Tram Loading
D-G: Various Disney Bus Loading Bays
H: Off-Site Shuttle Drop-Off/Pick-Up
Although gates can change, in my experience the buses to Disney's Hollywood Studios and Disney's Animal Kingdom parks usually stop in area "F".