Well, if it's glass your options are limited. Very fine scratches, the kind that appear as a general haze, can be polished. Deep scratches or gouges cannot. Years ago (like 40) the polishing agent was diamond dust. I did this on car windshields. We mixed it into a slurry with water and used a very dense rubber-like disc on a slow rotary buffer. Today the preferred polishing compound is cerium oxide - the same stuff used to polish lenses, and it can be used with a rotary polisher or an orbital polisher. It takes a lot of time and patience - figure a couple of hours to do an average size auto windshield. I just did a quick Google search -- polishing glass windshield -- and got 466,000 hits. The first page shows all kinds of kits and polishes and cerium oxide. Finding useful references should be easy.
The question that should be on your mind is how did the glass get scratched in the first place.