Just think Civ, really. It takes a little getting used to, but keep at it and you'll figure it out.
The early turns are basically going to be a rush for planets. You're going to be concentrating on getting some colonies out there, trying to find habitable planets. Early going is tough because you have virtually no population to tax and do your production and research. Once people start gettin' busy, then you'll have more to work with. You'll start to realize you want certain technologies to help you out, you'll work at getting those, then you'll start running into other races (maybe) and finding stuff as you send scout ships and whatever around to explore. If you do military you'll start researching weapons, if you're going for exploration you might start working on engines and life support to extend your range. Either way, once you get that far your situation will probably dictate what you feel like doing, or maybe your chosen end goal for winning. I tend to be more pacifistic, focusing on getting tons of culture spread and enveloping a lot of territory with my influence.
So yeah: early game, colonize. It'll feel like an awkward balance between getting your guys out there and spread to new planets and actually keeping a population on your new planets, which will struggle in the early stages because there are so few people.
Then get the lay of the land, work on setting up some kind of general infrastructure around your territory, even if its only mental. If you have neighbors, see what they're up to. Start working on research in more earnest, figure out what direction you want to head in. Look at your situation and think about what you need.
By then military will start to become relevant. You can probably get away with all but ignoring it initially, and in GalCiv you'll find that diplomacy goes a long way. Wars don't tend to jump you, they tend to creep up toward you. If you've got a good diplomacy rating and have learned some diplomatic research items, you can really work a lot of stuff in your favor and stave off hostilities. The United Planets (kind of a space UN) is cool too, allowing you to occasionally manipulate the galactic community to your advantage.
Just keep at it, you'll figure it out. With planet enhancements, remember to read what they do. They aren't always totally self-explanatory. You won't need farms until your planets need to expand their population caps, for instance. Factories give you an extra 4 (I think) resource points to work with, but they don't increase your actual production rates by default. The marketplace things give you a 10% increase in economy. So read the specifics, that can help. And don't be afraid to build stuff when you need it initially and then destroy it later. That isn't always feasible, but sometimes it can help you out. And remember that you can buy stuff you're building to get it done faster, but not only that, you can also finance it. Depending on your strategy, that can be useful.
EDIT - Forgot to mention... use the shipyard! Once you get the hang of building ships, it's super handy. You'll probably not want to wait for new ship designs to get all the component parts before you build new ships. I mean, if you get a faster, smaller engine that none of your current designs have, you may well want to just rebuild those designs with the new engine. It's quite easy and streamlined. A bit annoying since "updating" a design doesn't actually let you start with that full design and then subtract/re-add (it just starts you with a bare hull, so you won't know exactly what was on that ship unless you knew already)... but it isn't rocket science, heh. Fiddle, you'll get the hang of it. Engines make you go faster, life support lets you go farther, sensors let you see farther, and various kinds of defense defend against various kinds of weaponry. You'll figure it out. Just build a lot of ships and have fun with it. Don't be afraid to use the "obsolete" function on old designs and make newer, cooler ones, even if you only got a few new items to make a new ship with. I tend to wait until I need a new ship for something, but then any time I do I just build a new design for it. This isn't often military stuff for me, so I tend to build newer colony ships that go faster when I get new engines, same with constructors, and sometimes stick on extra cargo space for something or what have you.
