cheapest way to get out nail polish from rug?

Blot, don't rub, or you just spread it into a bigger ring. Scrape off whatever is still wet with a spoon first. Then non-acetone remover on a white cloth, dab, move to a clean bit of cloth, repeat. Test it somewhere hidden before you start though. Acetone actually dissolves acetate and triacetate fibres, and some cheap rugs have them. Finish with a bit of dish soap in warm water to get the remover out, and blot dry with a towel.