There is no one true way to learn AJAX development. The best way to get started is, well, just to get started. The absolute minimum you need to know is,
Read up on Function#apply and Function#call,
- Learn the basics of the DOM and CSS
The DOM is just a big tree of nodes with properties. In combination with CSS this gives you the visual page that you see in the browser. Using JS you can add visual effects and create/remove new node structures on the fly. See http://books.mozdev.org/html/mozilla-chp-5-sect-2.html
Events are how people interact with your page/application. Most frameworks provide helper/lib calls for handling this, but using them is pretty pointless if you don't understand the underlying behavior. http://www.quirksmode.org/js/events_properties.html
There's a lot more to learn, but this should get you started. If you want a depressingly long list of skills you need to master, try this SO question,
The most important thing is just to get started. Build some trivial hobby project and you'll find the most important things you need to learn fast enough.