The way I picked up AJAX was by looking of some of the simpler articles on the basics (don't worry about cross-browser to start with) around the web. The basic concept is quite simple and it is easy to get up-and-running if you have experience with client-side and server-side scripting.
For me, the firebug tool for firefox was indispensable as it allows you to see the requests that are being sent out and received from the server, information you have no easy way to get at without such a tool.
Once you are up and running with the basics, the magic of AJAX will no longer be so mysterious and you can move on to one of the frameworks for adding cross-browser compatibility (I like jquery personally).
For me, the firebug tool for firefox was indispensable as it allows you to see the requests that are being sent out and received from the server, information you have no easy way to get at without such a tool.
Once you are up and running with the basics, the magic of AJAX will no longer be so mysterious and you can move on to one of the frameworks for adding cross-browser compatibility (I like jquery personally).