momandseandodisney and antkim -
The Private Dining experience is set up through the private dining person at GF. If you call the GF Front Desk and ask for the Private Dining coordinator, they will connect you. The WDW-DINE number can get you the number for the front desk. (I looked but don't have it anymore as it was 11 months ago now!)
It's a pretty easy process...you can choose your location (from 3 different areas), your menu (from any items on the menus at any GF restaurant), and there is a minimum dollar amount that covers the services of a private "butler" or server. You do not need to be staying at the GF, and they have back-up locations in case of bad weather. Also, you can pretty much request anything that you can think of to make your experience special! From rose petals on the table, to a customized dessert...Disney'll make the magic happen
Anyway, the coordinator will help you plan and discuss your options. Everything will be confirmed via email and you give your credit card (I asked to give mine via phone, as I didn't want to send that in an email) as a guarantee, but you won't be charged until your event occurs. They include 18% gratuity.
I hope that covers some of the biggest questions...and I hope it helps you plan a memorable event! If you have any other specific questions, please feel free to drop me a PM! Have fun!!