You can book what is called the Fantasmic Dinner Package at three Disney-MGM Studios TS restaurants: H&V, Mama Melrose and The Brown Derby. I think H&V is the least expensive (buffet) and I know The Brown Derby is the most expensive. They do require a credit card at the time of booking and will charge it $10 for each person in the party if they don't show for the ressie.
You book it by calling 407 WDW-DINE and requesting it at the restaurant of your choice on the date you need. You may need to be flexible, particularly if you're already inside the 180-day window.
Essentially, you dine, and when you pay for your meal you are given a ticket and directions to a "secret" entrance to the Fantasmic stadium. Reserved seating is on the right side of the stadium. You still need to arrive at the Fantasmic entrance 30 minutes prior to the performance, as they will release the unused seats to all guests about 15 minutes prior to the performance.
There are no rain checks if a performance is cancelled. Hasn't happened to us yet. Cancellations are rare--only if there is potential danger to the cast members or audience due to weather or equipment malfunction.