If you have an embassy or Marco Polo/UN you can see the Intel screen for a civ. Check what they are researching, and also whether they are Militaristic or Civilized. This will determine what tech they want the most. Tech gifting improves their attitude toward you, slows down their research, and can speed up your own. Your Power Rating is displayed at the top of the F3 screen; you see theirs when you start a diplomatic exchange. The earlier you set up alliances the more likely they will succeed, before the AIs meet each other and form "animosities". Use your Power Rating to determine which civ is your KeyCiv (it could be yourself as well) and make sure you do not get too far ahead in techs relative to them. This will keep the beaker cost down for your next research. I also recommend a simple utility called CIV2PLAN, which is available from the Utilities Download section of CFC. You input any starting techs and it shows you the list of techs that will be available at your next research choice. This allows you to plan critical-paths to important techs, like Monarchy, Trade, Philosophy and MonoTheism (my usual generic tech path).
The tech gifting or exchange screen will give you two tech options: the first is more "desired" by the AI, and sometimes they will refuse the second (but not often). To get an alliance, gift, or map exchange you need to get their attitude higher than Receptive; getting them to Worshipful will guarantee whatever you want, if they are able to do it. You cannot exchange maps without both having MapMaking first. You cannot get a gift from an ally whose power rating is lower than your own. And there seems to be some limits on number of alliances you can have at once, relative to your power rating too. As you say, it is an art rather than a science (although there must be some formulas built into the game that control the AI reactions). There are many more helpful tips spread throughout the CFC and Apolyton threads; unfortunately the Search functions are often disabled due to site overload. Joining in the GOTM or Democracy game discussions will bring most of the good information forward.
I find Fundy only useful for all-out, forget-the-research warfare, often after the SpaceShip has been launched. Bribing is more expensive but still doable so protect your own cities. All of the AI attitudes will drop when you launch, so take special care of your capital. "The best defence is a spirited offense"...
The tech gifting or exchange screen will give you two tech options: the first is more "desired" by the AI, and sometimes they will refuse the second (but not often). To get an alliance, gift, or map exchange you need to get their attitude higher than Receptive; getting them to Worshipful will guarantee whatever you want, if they are able to do it. You cannot exchange maps without both having MapMaking first. You cannot get a gift from an ally whose power rating is lower than your own. And there seems to be some limits on number of alliances you can have at once, relative to your power rating too. As you say, it is an art rather than a science (although there must be some formulas built into the game that control the AI reactions). There are many more helpful tips spread throughout the CFC and Apolyton threads; unfortunately the Search functions are often disabled due to site overload. Joining in the GOTM or Democracy game discussions will bring most of the good information forward.
I find Fundy only useful for all-out, forget-the-research warfare, often after the SpaceShip has been launched. Bribing is more expensive but still doable so protect your own cities. All of the AI attitudes will drop when you launch, so take special care of your capital. "The best defence is a spirited offense"...
On the other hand, I have 29 cities of my own, 73 techs, over 10K in funds. 
Think I'll have to commit to a choice of winning soon.
