If I sign up for a torrenting site like torrent galaxy or something

That’s a public tracker/index. You don’t need to sign up at all to connect to a public tracker swarm.

and leave my computer running then will other people get seeded?

Yep. You can set bandwidth limits if your upload and/or download internet package is bad so it doesn’t interfere too much.

Or do I have to upload a file or can I just have it finished?

Hit and Run is considered bad manners and selfish behaviour. You can get away with it on public trackers, but private ones typically ban you for that. It’s called leeching. It’ll be based on your total upload/download stats, or your ratio in other words.