If you are in MK - take the monorail to the TTC and catch a bus to DTD.
If you are in EPCOT- walk (or boat) to the BC/YC (1st stop) and get a bus to DTD.
If you are in DHS - take the boat to the S/D(1st stop) and get a bus to DTD .
If you are in AK - take the bus to AKL (close resort) and get a bus to DTD.
Leave at least 1 hour to get to DTD from a Park with the above transportation.
OR - hire a taxi at any Park and pay for your ride to DTD (maybe as high as $25 depending where you are traveling from) Ask the price of the ride before you get into the taxi and also make sure the taxi driver knows the way.

We took a taxi from the Dolphin to the Contemporary for our anniversary dinner at Cali Grill. The 1st taxi driver asked if the Contemporary was near MK. We asked if he knew how to get there - he said he need directions. We got out of the 1st taxi and went into the next taxi in line.

The 2nd taxi driver knew where the Cali Grill was and said some taxi drivers only know the way to the airport, since that is a larger fare they can collect.