As mentioned, if you want to speak with a live operator, the number is 1-407-WDW-DINE. If you are staying on property, you can make your reservations 180 days out from arrival and can make ten days' worth of reservations with that one call. You'll need the Disney accommodations reservation number, a telephone number, name, and how many in your party.
If you want to give the online reservation system a shot, it can be located here: Disney Online Dining Reservations
. While I haven't actually made reservations via this system yet, you should be able to make the first ten days of your trip in all one booking if you are staying on property at 180 days out.