You get in touch with Disney Dining, promise them an obscene amount of money, and show up at your appointed time.
DD7 and I did this last year and enjoyed it. We also had Jason Surrell as our Imagineer and he was very personable, making sure that DD got to get a question or two. That was nice - she was interested in asking about how he got started and writing and inventing and such while the others at the table were more the "On page 16 of your new book, Jason....." types. (Nice people, just on a different level of Disney wavelength) I don't know if we'd do it again, but it was pleasant and the food was excellent, for sure.