Generally speaking, decide how you want to win when you start the game. If you're going for a tech win choose your racial abilities to support that and so on.
I always turn my homeworld into a manufacturing powerhouse to pump out colony ships/constructors then it will go over to military production. Start with factories and leave some room for a manufacturing capital/other special stuff later on.
Keep an eye on your economy, I always build a marketing centre/equivalent on each world to bolster income. If you go broke you're doomed. Don't be afraid to adjust your tax rate/spending sliders in the financial screen either, early game I ramp up the tax/spending sliders to kick research and production into overdrive and adjust them as things develop. Your spending goes up as your colonies complete structures so you will see your income dropping. That's when the market structures come into their own to offset this.
I tend to create a 'capital' planet for Manufacturing (homeworld), Research and finance. Each world will be given over to the relevant structures and I shove the matching capital structure on to make the most of them. Other worlds may be more multi-purpose.
No matter what your intended victory goal is maintain a decent sized defence fleet. Having a competitive military will greatly reduce the chance of you being attacked and lets you focus on your objective.
Trade is the greatest diplomatic weapon in your arsenal. If you have trade routes with another race they are unlikely to attack you as doing so threatens their own economy. If you're going for a non-military win then trade with everyone.
Choose your wars carefully. Attack the wrong guy and you might discover he has friends.....
Hope those basic pointers help. Good luck!