The headlight restoration kits contain a little 2000 grit sanding pad, an either slightly smoother or rougher pad (can't remember atm), the polisher drill attachment and plastic polish.
If you already have some sort of buffing pad, you can just buy the plastic polish.

You're probably going to need more sandpaper anyway. You might need to start out with a more aggressive grit depending on how deep the scratch is.
Basically what you're going to do is sand the the scratch until the area around it is just as low as the bottom of the scratch. At that point, the scratch will no longer be discernible from it's surrounding area. (it will all look messed up) Then you'll use progressively finer sandpaper to make the scratches created by the previous round of sanding smoother. When you work your way up to 2000-3000 grit sandpaper, you can then move onto polish (which is like even finer grit sandpaper). The polishing stage should make it clear again.
It's a lot of work removing enough material to get past the scratch, then getting the surface smooth enough to be perfectly clear again.
Personally, I'd rather just pay the $30.