Welcome to CFC, Romans!
Tech speed and commerce are inextricably linked in Civ 3. Beakers produced = commerce x science slider. I don't know what level you're playing, but as you've just gotten Civ 3, I'm assuming that it's one of the lower levels. If you're falling behind at Regent or below, then here are some common culprits:
1) Too many unnecessary structures. Paying maintenance on buildings cuts into the amount of gold left to go into science.
2) Too many unnecessary defensive units. Once you pass the unit support limit, every unit costs commerce & that cuts into the science budget.
3) Too few workers to build roads. Roads add commerce.
4) Too few roads. Roads add commerce.
5) Ineffective research strategy. Research left to right, not top to bottom. That will give you better chances to get monopoly techs, SGLs, and trade opportunities.
6) Ineffective trading. You're just going to have to quit hoarding techs. Trade carefully, but learn to trade. The AI civs will trade amongst themselves, whether you do or not. You might as well take advantage of opportunities.
If you really want to get some detailed information on your game, post a save.