Hi Illusion
This is probably obvious but dont forget that tech, happiness, food and gold are all related. Finding more luxuries or building happiness Wonders translate into faster techs. As do economic improvements. It is vital to explore early (with any unit you have available) and secure as many luxuries as possible even if it means building a few cities too far from the capital to be really useful otherwise at this stage. Also dont forget to check the research and happiness slider every move. You can often reduce science and stay on the same number of turns, especially when getting close to a new tech. You can sometimes get the last turn before an advance with tech set to zero and just one scientist somewhere.
Try and get the Great Library. As soon (or even before you get it if you are confident) set tech to zero and let the AI spend the money on research. Save gold so you can research and build faster when Education cancels the GL.
The other vital thing is micro-management e.g not wasting time irrigating a square in despotism when it does not give you more food.
You probably know all this stuff already, anyway good luck
Regards