1) War. This is definitely the biggest single advantage we have over the AI's. More land = more research power, and also means less for the one you're killing

. One thing I've learned about war is - better soon than later. Build an army and conquer AS SOON AS POSSIBLE. Even if you have to slow down your research and buildings. This means whip/draft a lot if you need to. The AI's are also less likely to declare war on you when your army is large... out of anything I find a large army prevents the AI from attacking moreso than being 'pleased'.
2) Tech trading - Although the AI's get large bonuses during trades, there is a good reason. The AI's tend to follow similar research paths, meaning you can plan out what you research in order to make trades. If you're worried about WFYABTA.. then I'd suggest ignoring whatever techs you don't need (dead ends like divine right or archery if you didn't use it early on). Also, you can try cultivating an ally because if you get friendly status they will trade with you no matter what.
3) GPP production - we can do this more effectively than the AI's. Light bulb techs and trade them back to the AI's if you are behind.
4) wonders - although they are fairly unpredictable, there are some decent things you can to do. Best economic wonders in my opinion: GL, pyramids (try to capture this from the AI, unless you really have ideal conditions for building it), great lighthouse (if you have a fair amount of coastal cities).
5) City specialization - Although sometimes the land does not allow for perfect GPP/military/science cities, this is another thing we do better than the AI. If you tend to run a CE, beauracracy + cottages + oxfords + academy generates a lot of science. Probably somewhere between 200-400 a turn.