It’s super easy. ShaderToy draws a rectangle on the screen and runs the given shader on it. There’s a small amount of plumbing to wire in a few variables like time & mouse position, and your texture coordinates. The rendering part of ShaderToy is simple enough that you can make your own clone in a day. The rest of the site is the hard part, the editor, the API & saving shaders in the cloud, getting lots of people to write awesome shaders, etc., but the rendering part is near trivial.