Toothpaste. Don’t use circular motions, apply from the center toward the edge, and make sure you completely wash off all of the toothpaste when you finish so it doesn’t eat away at the CD.
Wet sanding perpendicular to the tracks. Do a web search for “Digital Innovations SkipDr”. (And the spray bottle it comes with is just distilled water.)
I’ve used SkipDr successfully to fix scratches on old media I needed for work. Good product. Personally, I don’t really use optical media anymore as USB storage is so cheap now. I can fit a whole binder of data CDs onto a device the size of a fingernail (which doesn’t get scratched). Something to look into if you’re interested.
I once used vaseline. It doesn’t fix the scratches but it fills them in temporarily so I was able to make a copy of the CD. It’s much easier than the other methods.