In jewelry making, what is usually used to polish a dull looking semi-precious stone?

I’m new at this and don’t know much of anything about beading or jewelry making yet, just one wiring class at a local bead store. When I see semi-precious stones in other people’s handmade jewelry, the stones are almost always polished looking. I bought a strand of tiny amethyst stones various other pieces the other day to start experimenting with. But I noticed that the amethyst looks dull. I never see dull looking stones like that on etsy jewelry or at craft festivals. There must be a way to polish or shine it up? Hopefully a way that doesn’t require buying even more loads of expensive tools materials, lol.

How can I polish/shine semi-precious stones? Can I just buy some kind of special liquid solution to rub onto the stone with a cloth to polish it? If so, is there also a special cloth I should use, or is any fabric fine to use? Thanks for your help!

fine jewelry