As afficionados probably know, Frisbee is a trademark owned by Wham-O, while a lot of the better options in the "flying plastic disc" market are sold by companies like Discraft.
The Flashflight Disc-O, designed in Boulder, CO and widely distributed by Nite Ize, is a good quality disc with an RGB LED and a couple of coin cells mounted in the center. A handful of fiber-optic light pipes run from the center out to the edges. At 185g, it weighs a bit more than a standard Ultimate disc, but generally flies well and has a good feel.
I decided to modify one of these since I figured I could repurpose the light pipes. They already look pretty good, after all:
Any decent disc should work for this project, but something that will diffuse or scatter light will look the coolest.
The Flashflight has an enclosure for its LED and batteries mounted on the underside. This also doubles as a power button.
First, pry the lid / button case off. You should be able to do this with your bare hands, but it's fairly stiff.
Remove the LED assembly, and you'll be left with a hard plastic enclosure, attached to the disc with little plastic globs / studs / rivets.
Get a utility knife or X-Acto and (carefully!) cut through the globs of plastic.
Next, we'll put together the electronics and make sure a basic lighting sketch is working before attaching to the disc.