I've written about the way sailors aboard WWII British destroyers experienced combat here. Much of what I wrote there is relevant to this question; there was not a universal experience of naval combat, even aboard the battleships. I've covered AA warfare and life in the engine room in that post, and as they were not significantly different aboard battleships, I won't cover them here. That said, I'd like to include the following quote on the former topic from Roderick MacDonald, a midshipman aboard Valiant off Norway in 1940:

We were both posted at the back of the bridge with binoculars to alert the captain. 'Bomb doors open, sir.' Then 'Bombs away!' He then put down the wheel hard one way or the other. It always worked, as the explosions and columns of water erupted where we would otherwise have been.

In the run-up to a battle, British ships were kept at high states of readiness. There were four states of readiness, used depending on how imminent action was thought to be. The laxest, the fourth, had just one of the main guns manned, or a quarter of the AA armament. The third degree, known as defence stations, had one of the two ship's watches manning half the ship's armament at any one time. In the first degree, the armament was fully manned, while in the second, the men could rest at their stations or groups were fallen out in turn to rest. The experience of this aboard the cruiser Birmingham in 1941 was described by the American observer Joseph Wellings:

The turret crews slept in their turrets. The 4" HA/LA (high angle/ low angle) crews stood watch as follows; 1 mount crew actually on watch with starshells ready to be fired on either side; 2 crews slept in the starboard hangar, about 40 yards from their mounts, 1 crew in the officers' galley compartment about 10 yards from the HA/LA mounts. LA control parties stood watch and watch - complete crews - additional men taken from the HA control which were not manned. Pom-poms and .5" machine guns not manned.

This could be tiring for crews, but fortunately, they did not have to endure it for long. Engaging a target broke a difficult tension, one aptly described by Henry Leach, an officer aboard Duke of York at North Cape:

Then came the long-awaited order 'All positions stand to!' In an instant, tiredness, cold and seasickness were shed and all hands became poised for their individual tasks. 'Follow Director', and the huge turret swung round in line with the Director Control Tower. 'All guns load with armour-piercing and full-charge- load, load, load!'; the clatter of hoists as they brought the shells and cordite charges from the magazines, the rattle of rammers as they drove them into the chambers of the guns and the slam of the breeches as they closed were music to all. Then a great stillness for seemingly endless minutes, disturbed only by the squelch of hydraulics as layers and trainers followed the pointers in the receivers from the Director. 'Broadsides!', and the interceptors, connecting the firing circuits right up to the Director Layer's trigger, were closed; a glance at the range receiver whose counters were steadily, inexorably, ticking down..

Battleships, with their heavy guns, had large turret crews. The triple 16in turrets of the Nelson class had a crew of 93 men. Of these, a gunner's mate, 15 seaman gunners and two other seamen were in the turret proper. Seven gunnery ratings and nine other seamen were in the cordite handling room, while four gunnery ratings and 21 seamen manned the magazine. A gunner's mate and eight gunnery ratings were in the shell handling room with another eight ratings and 17 others in the shell room. The magazine and shell rooms were directly below the turrets, with the handling rooms between them and the turret, with hoists connecting all of them. Shells were loaded onto the hoist in the shell room, which took them to the handling room. Here, they were placed onto the hoist to the turret, where they were loaded into the gun. The cordite charges followed a similar path. Introducing the extra step with the handling rooms was less efficient, but meant that there was no direct path between turret and magazine, preventing flash fires from turret hits causing explosions as had happened to three British battlecruisers at Jutland in 1916.

Once the guns had been loaded, they needed to be fired. British ships used a centralised director system to aim and fire their guns. Firstly, the ship's captain would use his sight to select a target ship. His sight would automatically pass the target's bearing to the director control tower (DCT), a rotating cylindrical edifice typically placed high in the ship. Here, three officers sat; in the centre was the control officer, who fired the guns at the correct moment. To his left was the rate officer, who observed changes of course or speed by the target, while to his right was the spotting officer, who observed the fall of shot and used it to correct the next salvo. There were also four-five ratings in the DCT. A senior rating, the director layer, controlled the elevation of the guns, while another senior rating kept the DCT pointed at the target. A third rating applied corrections for the roll and pitching of the ship. The fourth rating was a telephone operator, keeping the director connected to the rest of the ship. The fifth rating, if present, measured the range to the target, though this job was usually done by the rangefinders in the ship's turrets (these were wider, and thus more accurate, than the ones in the director tower). As the war progressed, radar began to assert itself as the main way to measure ranges to targets in all conditions. All the information - target range, bearing, speed and course - from the director was passed to the transmitting station, positioned deep in the ship. Here was found the ship's Fire Control Table, a complicated electro-mechanical analogue computer. Information was fed in by turning a handle, as described by Jon Pertwee, operating the High Angle Control System aboard Hood:

My battle station was down in the bowels of the ship winding a small wheel. Somehow with the aid of other wheel-winders our mutual endeavour enabled Hood's gunnery to reach a greater state of accuracy.

The FCT processed the data, and passed its results to the turrets, which were trained to match it. Once the guns were loaded and correctly trained, they were fired by the control officer in the DCT. Typically, fire was carried out in salvos; part of the armament was fired, allowing the next salvo to be corrected. The 'ladder' system was typically used to achieve the best results. In this, two salvoes were fired to find the target's bearing. Two more were fired to find the correct range, then further salvoes narrowed it down in 400' steps. Ted Briggs, a signalman aboard Hood, described her actions during the bombardment of the French fleet at Mers-el-Kebir in 1940:

The response was immediate. Just as I turned round to watch, the guns of the Resolution and Valiant roared in murderous hair-trigger reaction. Then came the ting-ting of our firing bell. Seconds later my ears felt as if they had been sandwiched between two manhole covers. The concussion of the Hood's eight fifteen-inch guns, screaming in horrendous harmony, shook the flag deck violently.

His shipmate, Len Williams, described what it was like to receive fire in the same action:

It was not a pleasant experience to be fired on, particularly when it is known that the projectiles coming your way weighed almost a ton. I, and most everyone else, was scared stiff. To begin with, my action station was three decks below, in an electrical repair party, and although we could hear the shells passing over us like express trains, we could not see what was going on. We did see our two wounded men being helped down to the dressing station below us, and their blood-stained appearance did not help us any.

The massive blast from the main armament could be bad for the ship, or for poorly protected personnel. The two Nelsons were particularly susceptible to this, as they had been lightly built thanks to the need to cut weight to stay within the bounds of the Washington Naval Treaty. At Bismarck's last battle, Rodney probably did more damage to herself than Bismarck did. The concussion from her 16in guns dislodged many of her fittings, distorted her deck, and broke glass plates and periscopes. A pre-war test of the armament of these ships was cancelled because the testers were reporting strange symptoms (seeing unexpected bright flashes) that were found to be caused by the concussion from the gun blast.

Should a ship receive a hit, damage control would need to be carried out. Damage control parties were typically drawn from the stokers - at any one point, two-thirds of the ship's stokers were not needed in the engine rooms - plus men from any unengaged part of the armament and other men with little to do. They were typically commanded by the ship's Commander (the Captain commanded the ship, while the Commander looked after the crew and was his second in command). Damage control might involve spraying water on burning fires, or pumping fires out of flooding compartments. Bulkheads in damaged compartments were shored up, though this was arguably not the most effective use of time and effort.

In general, however, fighting a naval battle was an exhausting, draining experience. Ted Briggs' description of his actions following the engagement at Mers-el-Kebir expresses this well:

When I finally got below at 22.00 the messdecks were quiet. Everyone was dog tired, and off-duty watches were collapsed all over the ship. Many, like myself, were too exhausted to sling their hammocks. I joined a bunch of friends dozing on top of the hammock stowage. They were still fully dressed, with anti-flash gear on.'