Arcalian,
You're doing one thing right - you're looking in the Forum for help. A lot of people have posted detailed techniques that you should look into after you get the hang of the game and the interface. Here's a couple of tips to get you started:
At the start of every game, check out your Domestic Policy screen. It has the 5 most important sliders in the game; your tax rate, spend rate, and the 3 proportional sliders for what you're spending on. Leave the tax rate alone until you have played a game or two. Most players posting here on the threads set Spending and Military sliders to 100% for the first dozen turns or so to build ships FAST. This means you're losing money for now, but that's OK as long as you have a positive bank account.
Build colony ships and maybe a scout or two as fast as you can until you can't find any more PQ15+ planets to colonize. Start with the stars near Earth and look for yellow or purple stars to find them. Don't put too much population into those colony ships, or you'll hurt Earth's production if too many people leave. 200 million or a bit more is usually OK.
After you've cranked out a few colony ships, you can fiddle with the sliders to start spending on science as well as military - say 50% each. Work on Communications Tech and Universal Translator first so you can actually talk to people when you find them.
When the initial colony wave is over, pull back on the military spending a bit and start working on social projects instead, but keep tech at 40-50%. You should focus on anything that helps your planets' PQ at first - soil enrichment and habitat improvement. As these start to shoot up your people will breed (!) faster, making your planets more productive.
Start thinking about defense at this point. Keep an eye on the Military graph on the right side of the screen and make a point of being near the top. A Corvette in orbit around each system is usually enough to start. Adding Defenders to key systems near the enemy is also good, especially if you're neighbors with the Drengin or Yor, who love picking on good weaklings.
Don't forget trade. It makes the difference between a marginal empire and one that's rolling in dough. Minors are GREAT trade partners if you're near one.
Whenever you're not working on military ships, build a constructor. Instead of a lot of weak starbases, concentrate on a few good ones that help both your trade routes and your culture rating for your key systems.
If you keep your tech spending up near 40-50%, and you weren't shafted on getting colonies, you'll find that you can usually out-research everybody at the low difficulty levels. Don't be afraid to trade ANYTHING that doesn't give a Diplomatic boost. ALWAYS try to trade for cash first, preferably for 20 months or more. It lets you overdrive your own economy while hurting the pace at which your enemies develop.
These tips should get you started. As I mentioned at the start, cruise around these threads - or on the GC Strategies board (tab is on the left side of this screen) - for more tips. Good luck, and good gaming! You CAN beat this thing!