I'd also like to take a stab at making a clearer tech-trading post. I'm going to ignore what others have posted so far, so this will be a bit redundant (except merlinme's example, which I'm stealing):
Your cities each produce a certain number of Research Points (RP) each turn (it's a decimal value, although usually you only see the whole value displayed). These RP are put towards whatever technology you're currently researching. If that technology requires 100 RP and you're producing 10 RP per turn, it will take you 10 turns to finish researching it.
Each time you finish researching a technology, you get a percentage (I think it's 30) of the amount of RP it took to research that technology in the form of Knowledge Points (KP) in the category that the technology was in (Civ/War/Magic). KP is a tradeable resource. KP you received from researching does you absolutely no good, but KP you receive from another faction is immediately converted to RP in the KP's category (so if you get Warfare KP, it becomes RP for a seemingly random Warfare technology). You don't get to choose what technology the RP you get from trading goes to. Even if you were researching a Magic technology and traded for Magic KP, the RP it becomes wouldn't necessarily go towards the specific technology you're researching (and it doesn't tell you what tech it goes to).
When you trade away KP, it's like trading away money, in that you lose it. Maybe it's best to think of it as documents for "how we discovered this", and you traded away your only copy of those documents. It doesn't really make sense from a realistic perspective.
So, the whole point of getting KP from researching technologies is to trade it to others. KP you get from trades is the same as the RP you get from cities, but you don't get to pick the specific tech it goes towards, only the category.
And that's all there is to it. You're basically just trading RP that you can't use for yourself. It's actually quite simple (just not intuitive).