What I always do to get ahead of the other civilizations is 3 things; Expand, expand, expand! Make settlers like your default construction and build as many cities over a vast area of land as fast as you can. After all, more cities, more people, more taxes, more science. And more science, more military tech, more military units, more likely you'll rule the WORLD! Myeah so that's my strategy. It also helps to build some cities along a rival's borders to try to get some cities on your side. Of course in my very first game of Civ 3, I suppose the french were slightly tee'd off by my culture taking over their cities so they sneak attacked me. I showed them by taking their capitol! But yeah, expand, expand, expand.