Annatar's points are great, I have done them all. I also have done tojka's tip by making hard ai's shades of red. Here's some specific tips I can add.
Defense is crucial in the early game for me. An attack by a few AI factions in the game is nearly certain. Watch for a scout, then a few light frigates, then many more light frigates with possibly a capital ship. When you see a couple of light figates, know that a larger attack is likely coming. Invest in hangers and repair stations at these points. You need something there to out right kill those light frigates, and tie up the larger invasions and pirates.
Keep your number of colonies low enough that one fleet can jump quickly to them ( I like to have a fleet one jump away). Generally this can mean having 3 or 4 colonies until your economy is up and you are building a second fleet. Until then you will be fighting in areas that are very favorable to you due to the repair stations healing your capital ships and the present hangers and guns. Phase inhibitors are useful too, as the enemy sustains high losses as it retreats and this can buy you a lot of time. I also steer away from light cruisers, and long range missle boats and go right for light carriers and capitals if I can. This is because they are far harder to kill and the repair stations are so good at repairing them.
Finally Vasari has a technology that allows a fleet to travel to any world they control from any other world they control via structures you can build (phase stabilizers). This allows one fleet to cover your entire empire.
