A sergeant is responsible for what?

There are several grades of Sergeant.. there's Sergeant, Staff Sergeant, Sergeant First Class (Army), Gunnery Sergeant (Marine Corps), etc..

A basic Sergeant is typically responsible for leading a fire team (four persons, including themselves). I've seen a lot of Marine Corps Squad leaders who've held the rank of Sergeant, though, and some in the Army (although they were usually eligible for promotion to Staff Sergeant).