There's basically 2 sides to the game. When you're not deployed, things run at whatever pace you want. You can craft, buy, and sell stuff, chat, set up a base, set up your army, etc. Nothing blows up that isn't deployed, so you can spend as long as you'd like doing stuff here.
When deployed, it becomes a turn-based strategy game. If you've played Final Fantasy Tactics or anything along those lines, the combat should be pretty familiar. As for what to do while deployed, that depends on where you drop, but you can kill bandits for xp, fight other players, mine, or get into faction wars. Exactly how the faction wars work depend on the planet (there's currently 4 types), but they all have some objective you're trying to complete, with pvp involved as others try to do the same. You can always work together with others when desired, especially on planets that allow bases, as you can land directly on the base of anyone in the faction.
Early on, you're largely going to be aiming to get established - getting some credits so you can buy stuff, picking up a few levels so you're a bit stronger, etc. The 2 newbie planets (Taris and Riona) both have short cycles, limited power levels of enemy spawns, and no pvp whatsoever, making them great for this.
What you're ultimately going to be aiming for depends on what you like. Some get heavily into the faction stuff, some like straight up pvp, some are more into regular combat, some aim for the crafting side of things, and of course, some do a little of everything. What you'll do in a particular session really depends on what current goal is - are you after money, xp, advancing the faction, getting into duels, building stuff... etc. Because most of the planets have short cycles, and because you can call a dropship to leave a planet at any time, nothing stops you from hopping from planet to planet and say... mining on Konu, selling the ore, buying a good unit, deploying to Aldus for some heavy combat, then finishing up with a quick Zebus run for the beacon for faction points. Since only deployed stuff is vulnerable, you can play as much or as little as you want to on a given day.
The game can seem insanely complex with the huge pile of units, mods, planets, etc, but once you figure out the core mechanics, it's not nearly as complicated as it looks.