#1: First turn in the game, change your tax rate to 100% science, 0 tax, 0 luxuries. Later in the game, when you have improvements sucking down your treasury, you'll be able to raise your taxes without hurting your science output much, but early game, this is critical.
#2: In order of most important first technologies, I go Bronze Working (Phalanx unit), Pottery (Granary improvement), The Wheel (Chariot unit), and Monarchy (for the government).
#3: Switch to Monarchy as soon as you get it. The tile production bonuses help immensely.
#4: Build granarys in your first few cities to increase their population, and thusly their outputs.
#5: Improve those tiles! If you're luck enough to get a two settler start, do not build another city with the second, use him as your permanent improvement worker, since he's maintenance free.