Having never played Civilization, I'm not sure what the similarities are. I can say that most of my thoughts on how to play GalCiv2 were comically wrong in the beginning. I played around and got fairly frustrated when I couldn't figure out the command to colonize a planet. Once I realized that there's no such command, things got better for me. 
I started with the campaigns myself, but looking back, I think I learned more and appreciated the game more in the sandbox games. Particularly, the Metaverse sandbox, which is basically a high score list where people can combine their scores in teams for a collective high score. It adds another dimension to it.
Essentially, you'll want to colonize planets in the beginning and keep an eye on your economy. You'll need to find a balance between expanding, research, manufacturing, military and economy. Luckily, there are quite a few ways to balance those things, depending on your personal style.
Do you want to be aligned with good, neutral or evil? Perhaps something inbetween two of those alignments? Does that even matter to you?
Play around with some sandbox games and ask specific questions. There are a lot of us who are more than willing to help if we know how you'd like to proceed. An evil player like myself also can give some hints for good or neutral games, so don't be too concerned with the alignment that shows up in the forums.
Have fun.
