I've passed from newbie to intermediate, so I can give some tips that helped me along as I went. I'll tend to start a game, just do whatever while I figure stuff out, restart after a little while, and repeat 3 to 5 times untill I've got everything down.
Once you got the basic start down, which others have explained, there are two things you should watch under the "Domestic" screen. First the resource slider, which is divided up between Military (building ships), Social (planet construction), and research (technology obviously). Don't neglect these sliders! You can just leave it at an even 34/33/33 split all the time, or you can give yourself a huge boost if you use it smartly. Like someone else said, if you're buying ships off the start, you can drop military spending for a huge research boost to push out those early techs. Or if your fleet is in more need of some tech upgrades rather than more ships, drop military and crank up research. Or if you're planets are mostly finished constructing buildings, drop Social, alternatively, if you want to crank out some buildings or a wonder, increase social. etc. etc.
One more tip that can be very important depending on the map you played, for constructing buildings. In my 'beta' game, I was playing on a mid-sized highly populated map. I got off to a good start with my colony ships, carving out a nice corner of the galaxy for myself, and as things progressed, started doing a lot of indescriminate trading, especially with the minor races. The problem came from all the 'building' technologies I ended up grabbing. Newer buildings are great, but they also take longer to build, and I had a lot of undevelloped land. Your economy is crashing, you need to build more economic buildings. Oops! Stock markets take 60 turns to build
After figuring that out, in my next game I'd upgrade to 2nd level buildings early on since those don't take too long, and populated the good majority of my open tiles before getting upgrades. Then depending on what you need most at the time you can research the new building tech, and the computer will que up all the upgrades on your planet for you.
One more tip I should add as you get farther into the game, keep an eye on the minor races planets. You can be friendly and play nice with them, but eventually one of the AI's will decide it's time to anhialate them. They usually have kick ass fully developed planets by then, and there's from what I can tell little repercussion for attacking them. And no warning that an AI is at war with them. Don't let them sneak in and conquer the little guys! Swoop in for the kill when they've crushed the minor's fleet, and you can add a huge asset to your civilization. Especially in smaller/less populated maps when planets are scarce.
