(...to die.)
If you can avoid killer crystals and ravenous space-roaches long enough to get a bit of a foothold in some backwater system, you can start expanding your empire further outward, exploring nearby solar systems and colonizing them to increase your sphere of influence and the size of your empire. And, for no well-explained reason, you don't spend fuel to zip around within your territory, only when flying outside of it. For this reason, expanding your territory is imperative, increasing the range of all of your ships.
Here and there, you'll find a wormhole. These are your express ticket to somewhere a bit further away... but as for where you'll end up, well, that's a surprise. Sometimes you'll find yourself in a new solar system with abundant unclaimed resources, sometimes you'll find yourself smack dab in an opponent's territory and more than once I found angry space-faring crystals or roaches that simply destroyed my ship on sight. Be warned: you will have no recourse if your ship is not a military craft. Unarmed ships (including delegate freighters) are just gone when they are intercepted. Go directly to oblivion. Do not pass Go, do not get so much as an option to attempt to retreat.
So, you'll want military ships. And you can build them as they are specified, or you can design your own ships from several provided hulls in order to create a fleet that has what you really want to bring into battle. There are various modules that can be used to loadout your ships, including different types of armor, weapons, engines, sensor arrays, powerplants, capacitors and crew modules, among others. Basically, the shipyard in StarDrive 2 has a lot of the feel of the ship-building aspects of Gratuitous Space Battles, the difference being that in GSB, you basically design the ships, deploy them in battle and then watch to see what the outcome is... and that's the entire game. Although not nearly as pretty as GSB, this one aspect of StarDrive 2 approaches that game's complexity. And, the tutorial claims that designing your own ships is a vital part of the game. Based on the amazing speed with which my ships churned out with the default design can be utterly obliterated, I am guessing that's a true statement, but this amount of complexity and investment is a bit much, in my opinion.
There is a Space Battle mini-game, which can be selected as one way to resolve an encounter when you meet up with an enemy force (or, you know, space-roaches or something). This game is also accessible as a short stand-alone gameplay mode called "Battle Arena" on the Main Menu. This mode shows a smaller version of the galactic map, limited to the small area in which the conflict is occurring. You start with a region in which you can place your ships, then once placed, the battle starts and you can give limited direction to your ships, such as "go here," stay stationary/keep moving or short forward/broadside. There is also a Retreat option that I usually hit by accident, which starts a countdown timer until that ship can warp out. (The ship usually gets destroyed before the timer finishes, anyway, just FYI.)
The other way that encounters can be resolved is by simply selecting the "Auto" option. Other than the fact that "Auto" takes much less time than actually playing through the fight, I find that the other difference between these two options is that, on the rare occasion, when I choose "Auto," I might survive the fight. So, you know, there's that.