I would suggest tracking down a Bluejackets manual (for US Navy) for the period, I have a 1943 printing, it gives a lot of information that the basic Seamen need and an overview of the Navy. It discusses things like the Watches, shipboard routine, tasks, the day in port or at sea, drills, etc. Next there are some great videos on Youtube, I follow David Bober for the Royal Navy, many show specific shipboard operations, general life and how things work, ships at sea, mostly 1960s British Pathe films, promos and such but a few Admiralty gems too dating into the war era. There is a good RN video on manning the helm, an older ating teaches the new guy, simply hilarious in a very British sort of way. And I found several for the USN that cover such mundane things as hygiene, crew compartments, how the boiler works, etc. Simply search Google, I found a retired USN Captain who made a chart of Divisions on ship, there is a great website discussing a Destroyer crew too, so keep digging.
Basically a ship is divided into Watches, both actual times of day that guys are on duty working, and dividing the ship for the crew. By job the crew is divided into Departments and these are further broken out into Divisions, sub-dividing the Watches and organizing the crew by specialty. At minimum you have Gunnery (all weaponry including aircraft), Engineering (the biggest division and everything that needs repaired or tinkered with), Damage Control (the First Lieutenant who overseas the hull, mostly merged with Engineering now), Navigation (often the XO is the Navigator and often also controls Signals and that included the flags, lights and radios), and Supply (the most senior non-restricted officer and often a catchall). Bigger ships get a Medical Department, the Ships Doctor heads it, on something like a Destroyer he may serve on the Flagship and a Medical Rating serve the crew of each other ship. Bigger ships get not just bigger crews but more specialized Departments, more Divisions and each head is higher ranked. Something like a Mine Sweeper with just four officers forces each one to oversea more than one area. Again the Bluejackets manual will give you an insight into how each man spends his day, normally it is one-third of your time at work, one-third awake and doing chores or eating and one-third sleeping. Each man has a Battle Station hat e mans and tasks for him to do, an unrated man might wipe brass fixtures and wash a deck, a rated man might tend a boiler, the Petty Officers are in charge of the men, the Chiefs in charge of the Division or Department under the responsible officer. Thus a warship has far more men than a merchant ship, every little ship function has a person to tend it, often more than one so it is manned 24-hours and can stay manned if men are wounded or killed in battle. All those extra guys usually provide muscle to move supplies when replenishing, man damage control parties or operate the light AA guns, and in port do maintenance. The modern navy is more technical and has trimmed manpower but back in the day the routine was drill, eat, chores, drill, do some job, clean or fix, eat, chores, sleep, etc., mix up the times done, repeat, with things boiled down to rather simple tasks. Every navy seems to follow the basic structure, after all most copied the Royal Navy traditions, but the differences seem less important than the similarities.