There are two answers, and they depend upon available ΔV (delta-V).
Realistically, there are only 3 weapons worth mention: Lasers, Missiles, and Particle Accelerator Weaponss (PAW).
Weapon ranges are going to be measured in megameters (1e6 meters) for missiles, and maybe a dozen kilometers (around 1e4 meters) for lasers and PAWs.
If available ΔV is low, then it's simply a slow drift together, and he whose fire control software and hardware works best wins. You'll never see the beams of the lasers or PAWs, only the effects of a hit. The battle will be a single pass. There may be some adjustment of formation, but its not going to be a lot. Missiles will be delivering nukes and will probably be used for generating detonation laser events instead of direct impact. (The available delta-V isn't enough to prevent the missile from being lasered before impact.)
If available ΔV is high (several G-hours), and the time is present to use them, everything has to be automated. A single pass, using kinetic kill missiles at high relative velocity. You send the missiles ahead, and use your lasers and PAWs for automated point defense. The goal of the point defense fire is to prevent the missiles from terminal guidance, not to detonate them, and secondarily, to disable the backup warheads. The missiles are armed with nukes, but that's only a backup plan; the primary goal is to actually impact, for the kinetic impact is huge. Maneuver is to avoid missile impact. The initial commit to battle is a sudden burst of missiles towards the enemy. And then, the missiles start to die. Next, the missiles or fragments impact, and massive crunches happen.
So, in either case, two formations approach each other, fly a single pass, and hope it's decisive. The next "pass" is going to be a way off in time... more like a second whole battle than a continuation of the first.
Silent, and sudden flowers of death. And a significant wait until battle ranges.
Onboard, in either case... program the computers, put on your vacuum suits, hit "commit", and then hide in the solar storm shelter, and wait. If there's still a ship after the battle pass, emerge, and assess the damage. Repair what you can. Find out which other ships survived, and match to grab survivors to the limits of your own life support systems.
The lucky ones die from near instant vaporizations.
The slightly less lucky die from shrapnel.
The least lucky are the guys who can't signal another ship, and fell off-ship during an impact event, and have no ship air, and realize that they are going to run out of suit air... and suffocate, slowly; floating there, waiting for death, praying for rescue, all alone in the dark...
Most people aboard ship will either live or die in groups - either the shelter took the hit, or it didn't. Some minor bangs and bruises in those that survived. The partials happen when the shelter is lasered open but not squarely hit... anyone in the wrong area is cooked alive near instantly; the rest see the hit. Fragments of molten metal floating in the remainder of the compartment cause minor holes and burns in the others. And, unless their radios are on, you hear nothing... despite their screams and sobs.
If detonation lasers happen, you can add radiation burns to those whose shelters were compromised. If the ship's point defense was overwhelmed, you're at ground zero of a nuclear flare... no cloud, just a bright light and vaporizing metal, plastic, and flesh. Chunks of ship disappear, and the survivors pick up lots of rads.
This isn't to say the ships are not maneuvering... they are. They are rotating to keep the weapons in arc, and spinning on the long axis to minimize laser and PA loiter times on any one spot. Changing facing is a series of pulses from a variety of RCS thrusters, timed to fire only when in the right position ... lots of small sudden jolts, not one smooth acceleration... Kind of a "throw you sideways" alarm clock effect. And when RCS engines get killed, it becomes an uneven tattoo.