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

It really depends on the individual Captain. Most will select the initial target and let the Gunnery Officer take over the rest of the firing and weapon selection, while they drive the ship. Some like to select the weapons, the ammunition used and call the shots.

It is the perogative of the Flag officer (admiral or highest ranking Captain) in charge to decide when to open fire.

The gunnery tower in a battleship is a pretty labor intensive, dangerous, and complicated place. There are petty officers on each level, a few officers coordinating firing and loading,and a Gunnery Officer in charge of the whole operation.

But the captain is responsible for the whole ship. The Captain orders which target to fire upon, and also when to begin.

Like any person in charge of hundreds of people, they only have to give simple orders and trust their subordinates to actually make it happen. They can merely day, “Shoot that target!”, and then they are free to worry about other things. How much they delegate varies, but in general they need only utter a few words to do virtually anything.

I’ve served on a range of Naval ships. The captain of a small ship works with the fire control officer to develop target selection and aiming solutions. Most of this is automatic because the ship is moving in all three dimensions + time while firing weapons. On small ships with strictly machine guns of various caliber the weapons are for defense only.

On Guided Missile Destroyer, a wide range of targets can be sent to Fire Control where the various missiles and other weapons can calculate target solutions and program missile launches. Most weapons systems, these days, are computer controlled with the addition of a ships motion computer that stabilizes the platforms.