But yeh, I don't really know how a turn happens, and what influence a design actually has on the outcome. Wouldn't want to make it harder on you.
(Tactical Layer)
I'm reluctant to go into any detail, lest I let the magic smoke out, but in brief, once its decided that there are ships in system shooting at each other, the outcome is largely decided by math, weighted by some dice rolling - but thats a weighting. Now, the people IN UNIVERSE can also do math, but they arent working from perfect information - they will sometimes decline battles that I know they would win, or the reverse.
We take into account weight, range, and type of fire, agility of ships, best attack profiles/ranges and the ability to hold that range and what youll give up to do so (Note that forcing a close risks exposing the nose, and forcing the range open risks exposing the tail. Crits there are worse than on broadside. Its not a 'never do this', but have a reason and know the risks before exposing those noses and tails). We pay attention to armor and SI (SI makes up a lot of a small vessels survivability, and helps keep small vessels relevant against their larger cousins).
Crits go into the math, but very roughly - all weapons have a small chance to crit, which climbs as weapon damage does and drops as armor thickness increases. Independent of this are the usual independent missile crit chances, which I have also given to the NGauss... 12, 11-12, and 10-12 respectively for L/M/H NGauss.
Fighters will be usually be used either defensively against enemy fighters (if inferior) or offensively in anti-shipping (if superior). Note that fighters are brutal against ships with light armor, damaged armor, and/or inadequate point defense.
(Strategic Layer)
The much larger question of WHO is fighting WHO, where, with what ships, and what objectives, is actually the more important one. We keep track of background history and whats happened in game, the personality and quality of national leadership, plug a RNG in to create some disruption, and look at national political goals and capabilities, and those of their enemies. (If you notice that no one is attacking the TH, its because they can do math. Each of you probably has at least 2-3 neighbors, and each of those neighbors the same. One of their considerations every turn is 'can I beat this kid up and take his lunch money'. Note we mostly exempt the TH from this in large part, because they are conquest-weary and unwilling to bear further costs for violent expansion. Mostly)
(Operational Layer)
Then its moving ship deployments around, based in part on what you told us was stationed where, and playing games with what information is available to both sides at what time to drive what decisions about what to move where when to achieve the goals we looked at above. Can you get word to your ships in time? Can they get there in time? Are there enough recharge stations to slightly speed its passing, or that of the messenger dropships? Do you have spare jumpships to form information exchange command circuits? (Communications lag is insane before HPGs come along). Its sensors and force appreciations outside of engagement range - do you break off, press on? Roll the dice against a more powerful enemy to try to punch through and burn the dropships and prevent the invasion? Or break off and make faces at them from outside engagement range, waiting for reinforcements (If you can! A faster opponent makes more choices for himself, and takes yours away... same for sensors)
One advantage of having two GMs is we smell-test stuff off each other. It doesnt make us perfect, but if each of us has an utterly hair-brained idea or outcome one time in 10, having us check each other theoretically makes that one time in 100. Smegish has pulled me back from the edge more than once and catches stuff I miss almost daily. I dont think he makes as many mistakes as I do, but I try to help, as well. :)
What we dont do is roll a d6 for Bob, a d6 for Jane, and then whoever rolled higher wins, which we then try to explain using in-game elements.