booyabazooka
F1 screen (domestic advisor) - there's a couple of sliders near the top, one has a "beaker" on it. Either drag it to the right, or click to the right of it to move it, and it will change your science rate i.e. the %age of your gold spent on science.
The screen shot below shows the important parts of the F1 screen ringed in blue -
the amount you spend on science (224 gold per turn), the slider (set at 50%), the current research topic (Economics, 3 turns to go), and the beakers produced by each city
In the city view, click on a worked tile. That citizen then becomes an entertainer. Click on the entertainer and they cycle through tax, science and entertainer. If on science that gives you one beaker too. But it's usually more efficient to work the tile and get the gold from a tile (if it has a road, or next to a river, for example).
To change the research, F6 screen science advisor. Just click on the tech you want to research.
warning abandoning part completed research is BAD - you lose all the accumulated research.
Faster research while ancient -
more cities = more money = more beakers
libraries = more beakers for one gold in each city
great libray = lots of free tech
anything that increases gold (roads, the colossus) = more beakers
more happy people (luxuries, for example) = less corruption = more gold = more beakers
better givernment (monarchy or republic) = less corruption = more gold = more beakers
edit - also good
pop open a "goody hut" i.e. walk into it with a unit, and the locals might give you a tech for free
trade with the AI, swap techs or buy them
meet the AI - the more people you know, the cheaper techs are that they know. So if you're on your own, it's expensive. If you know a bunch of advanced civs, you can learn what they learn quite easily.
Almost ANYTHING you do, except building military, will improve your research.
even military can help - if you beat up on another civ, they might give you techs in the peace deal
Note - you need all the required ancient techs to get out of the ancient era. The only ones not required, AFAIK, are Monarchy and Republic. You want one of those anyway, just to get out of despotism. But you don't need both, IMO.
