Naval jellies! Just how closely involved is/was the captain of a warship with the gunnery?

I realized that in Star Trek, (which, along with from this summer’s Battleship, constitutes the bulk of my knowledge of naval warfare – sad, I know XD) the ship’s captain is literally calling the shots, picking targets and selecting weapons, in addition to working out the ship’s path.
Now that I stop and think about it, this all seems like a bit much for one guy to do.