I like how there are two pages of responses and none answer the original question. I'm not really sure after reading the wiki either.

What I want to know is if I beat a player of X rating, how much does my rank improve?

Lets say I am 1800 rating and they are 1900 rating. When I win, what is my boost (assuming no other games finish for either of us?

I'm fine with a ballpark amount, but would be nice to know.

What I want to know is if I beat a player of X rating, how much does my rank improve?

The short answer is that it's complicated. But if you really want to know the details behind it, you can find the full algorithm and source code here: http://remi.coulom.free.fr/Bayesian-Elo/#theory

Hmm, I can't really make sense of that. It doesn't really say what the columns mean.

I wish this was explained in laymen's terms somewhere.

Actually, what I should have posted is this:

http://wiki.warlight.net/index.php/Ladder_Ranks_and_Ratings#Run_your_own_Ladder_Simulations

You can run your own ladder simulations to check what would happen in different situations. So if you want to know what would happen if you beat a 1900 player, just find the player who's 1900, add in a win against them, and check what your rating changed to.