Ajax is not a new programming language, but rather "javascript 2.0." Short for asynchronous javascript and XML, it is built around two things: making everything on the page accessible as though it were XML, and offering the ability to communicate with the host server without a page reload.
As always, though, everybody has different ideas as to how things should work. Microsoft has their way, and everybody else has their way. The latter generally conform to W3C (short for World Wide Web Consortium) standards. With a few notable exceptions, so does Microsoft. Where they differ is in the sheer volume of additional "stuff" they include in their functionality. But, that doesn't need to be discussed until later.
In order to use Ajax effectively, you must first learn XML: Extensible Markup Language, as well as knowing basic JavaScript and HTML. After that, it is simply a matter of learning some basic functionality and then applying impeccable logic to whatever applications you should want to apply the concepts of Ajax to. But first, XML.