[PvK]

Getting the killing shot with a direct-fire weapon generally gives +1 experience to a ship. This works in all modes of play.

Destroying drones and fighters, and I think even using seekers can give some experience too, but it's much less. The game does track experience at a finer grain than full visible percentage points, but for practical purposes, ship experience is just +1 per killing direct-fire shot.

Fleet experience is also tracked on partial percentage points. A good battle often gives up to about +1, but any battle gives some - it may take a few before you get a +1. I think battles with fewer opponents, and/or battles where you outnumber the opponents, may give less. Battles which involve planet capture seem to give a lot less too (or maybe it's just battles without enemy ships). I think fleet experience is also divided between all the friendly fleets in the battle.

And playing as a "captain" or "fleet commander" is pretty much my favorite way to play SE4 single-player. It's a lot of fun (and very challenging, unless your AI is best) to try to tip the scales as a single commander. However, the Resupply Minister IS a big pain in the aft thrusters! My best solution to that is to commandeer a supply ship. You might also want to disable mines in the game... or else be really careful about scouting ahead to avoid dying to mines - I was having a great game of Proportions as a captain when I led an expedition through a warp point and we were all wiped out by an AI minefield.

Oh, you may want to rename a fleet to "Captain X" (your character's name), and then use it to represent your character in the game, so you can track experience and transfer from ship to ship.

You also might want to run enough turns until the ships and situations involved are interesting.

I recommend using as slow a research rate as possible, though, since the pace of operations as a commander means your ship will tend to be out-of-date after every cruise or two, otherwise.

PvK