Ok, You have to do 'all' research yourself on chief and warlord. The AI will 'help' you to some extent at regent. Monarch and emperor AIs are decent wrt research.
Your research capacity is mainly a function of the gold you generate.
You generate gold by working rivers, roads and commerce bonus tiles (think gold hills, ivory, furs etc).
Some govs are better 'gold makers' than others. Republic and Democracy are the best in that apartment.
There are multiplier buildings for both commerce (markets, banks and stock exchanges) and research (libraries, universities and research labs).
Do you have tons of (useless) units like warriors in middle-modern ages? They do cost you in most govs.
Trade with the AI to your advantage.
Do you build every improvement in every city? This is not necessary nor cost-efficient. Dead corrupt cities will only generate one gold and one shield no matter what improvements you build (this is not entirely true but use it as a guideline).
You may use specialist citizens (scientists, taxmen, hardhats) in those dead corrupt cities to gain something.
That's just a few tips. There are certainly others but I don't have the time to post more right now.
