lorddune, Here is some advice, whose main purpose is fast (early) military expansion:
Never build defensive units, only offensive ones. Just reflect on all the turns defensive units spend just standing around, doing nothing, giving nothing. In despotism, monarchy, feudalism they give a small boost to happiness as MP, but we can get that from captured luxuries or war happiness. Some players say that they like to build some defensive units and/or catapults to escort the offensive units. But I think this is normally completely unnecessary on all levels below demigod and of minor importance even on the higher levels. Instead, put a swordsman on a hill or a mountain when you move it into AI territory, and the AI wll probably not even attack it. Use the protection of borders so that the AI can move into your area but not attack, and you can easily pick them off next turn. But on the other hand, don't hesitate to sacrifize a few pawns. (Or, to buy time, send out captured workers and let the AI take them instead of wounded troops.)
Avoid the construction of buildings altogether, except barracks and forbidden palace. Aquaducts, for example, are way too expensive. Try to place as many towns as possible on rivers, and let those towns grow. Let the other towns build workers and settlers when they approach size 6, or let them work mountains, forests and hills with 0+ food but high production, and you have lost nothing or next to nothing and saved much time. Of course, there are exceptions to the "no buildings"-rule. If you go for domination victory, temples or libraries can more than double the territory of a town. (But there is little reason to build these until late in the game, when you are near the domination limit.) Secondly, diplomatic or spaceship victory will obviously require libraries, unis, etc., and maybe even courthouses and acquaducts. But there is no reason to assume that these buildings should be built before you build a sizeable offensive military. In PTW, conquering an AI and placing a forbidden palace in its ex-territory may well double your total research capability. And even though this means that you will have to build libraries later, it's worth remembering that if you fall behind in research in the ancient age, you can often trade your way up again. This brings me to my last piece of advice: Anticipate what the AI will research so that you can trade it instead of researching it yourself. There is an article on this in the forum called something like "What will the AI research next?" if you want details.
I consider it my biggest weakness in civ3 that I play it too safe.