What advice and or material recommendations can you give me about soundproofing without drilling into walls?

Renting a place. It’s small and I want to sound proof it. I’m thinking moving blankets or rugs/carpets.

What do you guys think? — I don’t have a reference picture but think a perfectly square room 15x15ft with wood or vinyl flooring (not sure).

Can I just throw carpets everywhere? Are moving blankets better or should I build small wooden soundproof panels that I can lay against the wall. Maybe both? Or maybe something else.

What should I do?

Edit: My goal is to control the sound leaving the house.