((Disclaimer -- I am a noob. While my ideas may not coincide with your own, I'd rather you share yours here than criticize my own. Please post your strategies an tips, I'd love to hear them.))
Trading:
Never trade diplomatic technologies. If you can hold on to these you will retain your advantage in trading.
Never attempt to trade for military technologies. The computer values these much higher than they are worth.
Ship building:
Build small and build early. Your early scout ships can be upgraded into tactical fighters later. The benefit to this is you don't end up wasting your early game production and your scouts / survey vessels will already have a jump on exploring the galaxy.
Colonizing:
Buy your first factory on a planet to jumpstart your economy.
Don't forget that money in your pocket is money wasted. Use it to finish up upgrades or ships whenever possible. The only exceptions would be if you are saving up to quickly finish a Super Project, or anticipating a fleet upgrade once a new technology is researched. Use your money wisely!
Sliders:
If a planet has nothing to build feel free to specialize in research or military production. Put tax dollars to good use! Meanwhile, research an infrastructure upgrade to get that planet back to work.
Approval & Happiness:
Keeping your citizens happy on each planet is a MUST. You can increase your tax revenue limitlessly as long as your citizens are happy.
Research:
Balance when you research infrastructure technologies and when your planets can actually make the upgrades you research. If you research too many in a row your planets will bog down with upgrades.