Ok, you are going pretty deep into the game. YOu have to either beed strongest or have friends, once all the land is grabbed,
You did not mention many details of the settings. Size, number of civs, water, pangea/contients/archi? Barb settings and what civ you are playing. When you say civ3, I presume you mena no addons, PTW or C3C.
Regent is the first level that you play with no handicaps in your favor. After Regent the handicaps go to the AI. This means it will play better than it did on Warlord or Chief.
So you need to play a bit smarter. First consideration is the city placement. If oyu were using wide spacing, stop now. Switch to CxxC. Pick your sites better. Get more workers and use them better.
Be alert to trades and skip some optional techs. If you ar enot going to Monarchy, don't other reseatching it. You do not need the HG.
Get out yourself ready to switch out of despotism quickly. Trade smarter, try to get a tech no one else has and trade it to everyone on the same turm.
It is hard to know what else to cover with out some saves to look at. Early ones as well as later ones. 1750BC or 2100BC, before you get too far into the game. As well as when you run into problems. So hold onto a few saves.