Colored material. This can acquired from a variety of sources. The simplest solution is to get some clear plastic and color over the top of it with watercolor or even a Sharpie. Translucent colored paper also works. If you want something a little more professional, you can do as the author of this Instructables article did and get a pack free gel filter samples from a filter company! Another pioneering author used a laser printer and transparent film to create their colored gel.
It's OK if the material is a little battered—none of those scratches or inconsistencies in color are going to show up in the final product because the light will diffuse somewhat.
Flash Mount. Here's the tricky bit. How do you get this bit of colored material to stay in place over the flash itself?
If you have an external slave flash, this will probably be a bit easier: a fitted cardboard sheath, a translucent film canister, any number of things can fit your purposes, as long as there's something to slide over the flash piece. Ditto for large pop-up flashes on the camera itself. Translucent film canisters work especially well for this purpose.
If the flash is built into the body of the camera... well, you might end up using a somewhat cruder solution like tape to keep the filter attached to the camera. There's no easy way to fit something over the camera body, especially compact camera so that it doesn't impede function.
Check out this article on various DIY filter mounts for lenses for inspiration on different ways to attach things to your camera.
Cutting utensil. A utility knife is your best friend in this department. Something that can cut plastic.
Glue. You'll want something that will dry as colorless as possible without expanding. The color flash won't be under too much stress.