From MK - Walk to Contemporary, catch bus to DTD
From Epcot - Walk to Beach Club, catch bus to DTD
From DHS - Walk or bus to one of the Epcot area resorts, catch bus to DTD
From AK - this one is a bit of a crapshoot since you have to bus to all of the resorts from there. I'm not really sure what would be best.
Of course, the fastest way is always to either drive yourself or take a taxi. But if you want to use Disney transport, I think that what I've listed should help you out.