Ginger Ale said to read all articles, and he is giving good advice. But if you are advised to do that, you probably won't. There is simply a lot of advice on there, and you will eventually itch to play too much and not finish it. While most of the info is very good, some of it is more specific. I am not a great player, I usually play on monarch, but I'll point you to the articles that helped me the most. Though I myself have not read them all. So, if I leave any out don't disreagard them, especially if their title deals with a specific trouble area.
The Four Rules of Wonder Addiction
Tutorial: Babylon's Deity Settlers
Cracker's Civ 3 Opening Plays Site
Expansion Tip: Outside In
The Art of War Q&A
Also before playing a specific civilization, check out Ision's Civ-specifc guides. I think reviews of all are now available.
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The best advice I can give is expand early and aggresively. If you don't start with pottery, get it immediately. I build two warriors (or scouts if expansionist) send 'em out and then (pre-build if necessary) a granary.
Afterward I alternate with warrior/settler (always protect your settlers) in my capital until my land is built up. The rest of my cities are focusing on barracks, defensive units, workers (lots! on a standard map I try to get about 10 in the Ancient age, and thereafter about 20-30), temples, granaries-in that order.
Then build up a huge assortment of either swordsmen, or horsemen, switch to Monarchy, and blitz my most powerful neigbor. I then take in as much of his empire as I want.
I take a break from war building aqueducts (if needed), libraries, marketplaces, and happiness improvements if necessary. Build my next generation army and go for the next most powerful bordering nation. I always win this way.