Hi there Steve!
How exciting that you're planning your very trip to Walt Disney World!
You can indeed reserve the
Fantasmic! Dining Package online via the Dining pages of the Walt Disney World or My Disney Experience website. It can't be booked using the My Disney Experience 'app' on your smart phone as a credit card is required to 'guarantee' your reservation (your card will not be charged at the time of reserving).
I've included the link just above that will take you directly to the reservations page. Reservation times for the package are actually always for 'early' dinners, lunches or mid afternoon, late lunches. When dining, your server will re-confirm your show time and present you with a voucher for your admittance to the reserved section at the outdoor seating area. Your voucher will also indicate the recommended arrival time and location of the entry gates.
My personal favourite way to do the Fantasmic! Dining Package is to choose a lunch reservation for Mama Melrose's Ristorante Italiano. We eat a light breakfast that day, enjoy a filling lunch at Mama Melrose's and then a lighter, quick service dinner. There are some great treats and snacks available to enjoy
during Fantasmic! so we prefer to arrive there not having just eaten a heavy dinner!
If you have additional questions, please feel free to write me back any time Steve. I'd love to hear from you again soon.
Wishing you a simply Magical time planning your first visit to Walt Disney World!
Kirsten