1. 4 city tradition ASAP. Get those settlers out quickly. Also, build the National College ASAP provided it doesn't hinder your expansion.
2. Grow as much as possible. More citizens means more raw science, which is the driving engine behind the game, but it also means more production and gold. The bigger your cities are, the better.
3. Beeline science techs. After you have your luxury techs, go to Philosophy, then Education, then Scientific Theory, then Plastics.
4. Work scientist slots. They give science and great scientist points, both of which are very important.
5. Rationalism. Secularism + Free Thought are a must. Sovereignty's ok I guess, but I like to use the finisher for Plastics.
6. Don't fall into the trap of wonder spamming. There are usually better things to build, and you risk getting beaten out to it. The wonders I would recommend building: Oracle, Pisa, Porcelain, anything with great work slots if you're going for CV, Hubble if you're going for SV, Forbidden palace if DiploV, Statue of Liberty if you have freedom.
7. In case this wasn't clear already: Maximize science. Science is the most important thing in the game. You need to beat out the AIs in tech.