A couple things that I try to do to help me in tech
1. Get acadamies for my best research cities. This means farming great scientists of course. Two quick ways to do this are to either build a library and run two scientist specialists, or build the great library which will give you great gs points.
2. Make use of great people to lightbulb techs, and then trade those techs. You can often be the first to theology or paper with a great scientist or prophet.
3. Take advantage of the two things that give you a free tech...build the Oracle or be the first to liberalism. A great scientist will help you get through Education quicker, as that always seems to be a "long" tech to finish.
4. Try to research techs that the ai doesnt have so you can trade. If all the ai's have iron working, for instance, try to research literature instead and trade for it.
5. Research alphabet as fast as you can. That tech lets you trade with the ai's. Usually if you are one of the first civs to alphabet, you can trade it for all the stuff you skipped...like animal husbandry, meditation, sailing, etc.
6. Run civics that increase your research. Representation, Bureaucracy, Free Religion, mercantilism to run great scientists, caste system to run lots of great scientists early on, free market for more commerce (research).
7. Build six universities as quick as you can. Not only will you get getting 25% more research in each city you build it in (plus the 25% you have from the libraries in those cities) but you will unlock one of the most important national wonders...Oxford University. This national wonder gives 100% research in one city, often giving you more research then you have in SEVERAL cities combined. Build it in your best research city.
8. Ive found that a huge help to my early research is getting Pottery asap and building cottages right away. Usually I build lots of cottages in my capital, especially on the river tiles because they already have 1

on them. They will give you a research boost once they start to mature, those river tiles often also have good food (grassland) or an extra hammer (plains), and cottage money will help support you building new cities without having to drop your research level to new lows. Then when you run bureaucracy you will capitalize on the 50% boost to commerce in your capital...you will have lots of nice cottages to boost.
9. Its not entirely reliable, but if you can, send out a second unit to look for goody huts. That extra money will help with expansion and research rate, but the best is finding those free techs.
10. If you can, try to settle cities near money resources like gold or incense. Thats great commerce for research.
I know thats a lot of stuff, but try a couple on for size. It will make a difference.