Call (407) WDW DINE. Call as early as possible. They book up fast and I don't believe you need to pay when reserving. They have plenty of standbys to take your place if you don't show.
You can also go to Guest Services in the park when there to check on 'standby' reservations.
call the resturaunt you wish to dine that that offers "character dining" and book in. Payment is required at time of booking and it is reccomended you do so at least 3 months prior to travel. These themed dining experiences are very popular, especially breakfast and dinner so get in fast to avoid disapointment later. You should also book in to any of the other main resturaunts such as the blue bayou etc if you really want to dine at them! Same guidlines apply.