Well, to start with, I don't know how you got two golden ages since the game is supposed to only allow one golden age. Next, I don't know what size maps you play but here are some general suggestions:
1. Build roads and make sure that you are using them. Build roads on tiles that are next to rivers, since you will get two coins (even in despotism) instead of just one.
2. To start with (i.e. when in despotism) use the general rule of irrigate brown, mine green. Also, remember that working a hill tile takes twice as long as a plains or grass tile, so wait to do that.
3. Link up resources, especially luxuries, so that you can use less money on your luxury slider. In warlord, you may even be able to do without using the luxury slider for much of the game if you get one or two luxuries.
4. Trade with the AI, but make sure that you get your money's worth. Some techs are worth a lot more than others. (You can look up my list or go to the editor of Civ III to see the cost of techs).
5. Try, whenever possible, to be in Republic (or Democracy) to get the extra money for research. However, remember that you want cities to be >6 when you are in Republic because units cost double in that government.
6. Do your best to create a settler factory early on (or two or three). This means planting a city near some food resources and getting a granary in the city. Even though the Pyramids gives free granaries, building a granary before the Pyramids is super useful.
7. Try to have a ratio of 1:1 for cities and workers. This is not critical, but is very helpful. Workers build the roads that give you the money that allows you to research.
8. Remember that it takes the same amount of food to go from size 1 to size 2 all the way up to size 7 for a city, so you do not necessarily want to have a settler built the very turn you get to size 3. In fact, that is not the best way to get settlers, wait for the city to get to a larger size and it will have more production to build follow-on units (settlers and troops).
As many, many people in this forum will tell you, reading the stuff in the War Academy of this site is very useful. I gave the above examples so that you could get started with your wins while going through the War Academy at your liesure.
