The first API script I wrote was pieced together mostly using the API docs. I learned quite a bit by looking at the sample scripts provided in the API (each page for a class has example scripts listed on it that use that class) and seeing how they used the functions I was interested in. It was still slow going, but the more examples I saw, the better I (hopefully) understood how to use it. And a lot of google searching to look for solutions or extra info on problems I was having (like how to us MScriptUtil and how to build different arrays).
The docs actually have quite a bit of info in them; I would also recommend reading through the API guide. Basically just read as much as info and code as you can and ask questions.
For asking questions you should join the python_inside_maya google group. It can be a good place to pick up tidbits and ask questions (Redirecting to Google Groups). They have no guides or walkthroughs or anything but I’ve picked up a number of tricks by reading other people’s API questions and the few I’ve asked myself.
And post about stuff you learn along the way! The more info out there to help people getting started (since they will undoubtedly run into the same problems) the better.