Tim's summary is pretty good, and the link to Samson's thread is the definitive detail. You also may not have heard about the KeyCiv; see this thread:
http://apolyton.net/forums/showthread.php?s=&threadid=2683
Some practical matters:
- "Turns to next discovery" is really "total number of beakers needed for next tech" divided by "number of beakers you are researching each turn". You can find the first number by setting your Science slider to 0: the "number of turns" it displays is really the number of beakers needed (make sure you do not have any Scientists working in your cities when you check). The second number can be found using F5; you can manipulate it a bit by moving workers onto tiles that have trade arrows and by adjusting your Science rate versus Taxes and Luxuries.
- There is no display of exactly how many beakers you have already researched beyond the rough "bar" display on F6, which becomes unreadable after 5 or 10 techs. Keep a running total by checking F5 at the beginning of each turn BEFORE you move any workers around. Add to that beakers from caravan deliveries.
- Map size (S/M/L) changes the multiplier between tech numbers. For Small it is 20 rather than 26.
- Techs that you get before your first move at 4000BC are "freebie" - they do not count against your tech number. Same for other civs, so if it seems you have gifted everything to your KeyCiv and you are still getting a penalty, they may have started with more freebie techs than you.
- Tech "costs" in beakers go up with each tech you get, whether researched, stolen, won in battle, traded for or discovered in a hut. Between your 16th and 20th they start going up faster, and at 20 they take a big jump, then go up by the same multiplier (20/26) for subsequent techs.
- If you "skip" a tech, like trading for Wheel without having Horse, it does not count against you, unless you need Horse as a prereq for some other tech.
- Great Library will give you a tech when the second or subsequent player discovers it. So if one AI discovers Gunpowder, you don't get it right away. When the second one discovers it, or gets it from a hut or in trade, then you get it too. If you get the GL, you do not automatically get older techs that you have neglected to research. The next time anyone discovers something, or trades something, if they are the second receiver of that tech you get it too.
- You cannot control which techs you get from GL, nor when you get them. If you are just about to finish researching MonoTheism and get a suprise tech from the GL, the number of beakers you needed to finish will increase. If you are near your 20th tech, it will go up significantly. If you get several one after another you may see MT put off 10 or more turns. Very frustrating for the planner types.
- The GL costs 300 shields. Four Libraries are about the same cost, and will probably produce more tech gains for you than the GL, plus you get to choose the techs developed. Or you could say that the GL is six caravans, and early in the game each caravan is nearly worth a tech by itself, if you are delivering fairly far away overseas.
- Building the GL is a good diversion for the AI. Let them work on it while you shoot for Colossus, Shakes and Copes in your Super Science/Trade City. Same thing for Pyramids and Great Wall. Once you have your SSC going, pass by Electricity early and obsolete the thing.
- My personal feeling is that I get more tech trades, attitude improvements, and map exchanges out of Marco Polo than I would get out of Great Library, and again Marco Polo lets me see ahead of time what they have so I can choose what I want. It's also cheaper at 200 shields.
BTW, Florian, welcome to CFC!