Hmm, I thought there was a nice article explaining RAs but I can't find it. Anyway, when an RA completes you get 50% of the beaker cost of the median of your currently researchable techs. This increases to 75% with either the PT or Rationalism opener and 100% with both.
As an example, let's say that you have 5 techs available to research that will take 4, 4, 8, 9, and 12 turns to research. Your median tech in this case is 8 turns, so an RA will give some percentage of 8 turns worth of teching, depending on whether or not you have the PT and Rationalism. If you don't have either one you get 50% * 8 = 4 turns worth of research, if you have 1 of those you get 75% * 8 = 6 turns of research, and if you have both you get 100% * 8 = 8 turns of research.
The part that trips most people up is figuring out what their median tech is. If you aren't sure how to do this I can go more in depth. Or if you'd rather watch a video, Wainy spends a good amount of time at the beginning of this video explaining how RAs work: http://www.youtube.com/watch?v=ip4YeME6wJI
As an example, let's say that you have 5 techs available to research that will take 4, 4, 8, 9, and 12 turns to research. Your median tech in this case is 8 turns, so an RA will give some percentage of 8 turns worth of teching, depending on whether or not you have the PT and Rationalism. If you don't have either one you get 50% * 8 = 4 turns worth of research, if you have 1 of those you get 75% * 8 = 6 turns of research, and if you have both you get 100% * 8 = 8 turns of research.
The part that trips most people up is figuring out what their median tech is. If you aren't sure how to do this I can go more in depth. Or if you'd rather watch a video, Wainy spends a good amount of time at the beginning of this video explaining how RAs work: http://www.youtube.com/watch?v=ip4YeME6wJI