The term "AJAX" is a little misleading and can easily confuse people trying to master it. The term itself really only refers to asynchronously retrieving or sending data from the server (i.e. without reloading the page), but it is usually used to describe any modern system saturated with Javascript. (In fact, even when you talk about receiving or sending data asynchronously, the term “AJAX” is not entirely correct - it was originally coined to mean “asynchronous Javascript and XML,” but most modern implementations use JSON instead of XML).
So, I suspect that you are actually talking about “modern Javascript”. Using Javascript on a website (as noted earlier) involves several related but different technologies, and is very useful when you begin to understand what it is, where they start and end, and how they interact.
First you have the Javascript language itself. Although there are several implementations, it is actually relatively simple, and you should have no problem finding the syntax.
Then there is the DOM or document object model. This is the Javascript-based browser interface for the page itself. The DOM is actually quite complicated compared to the Javascript language, and most likely this is the place where you have the most problems (not least because the DOM provided by different browsers tends to be slightly different).
To really start learning this stuff, I suggest you start by looking at the basic DOM manipulation. Learn how to dynamically create elements using the DOM, how to assign events, how your code interacts with the page, etc. The Internet has a huge amount of resources for viewing and several books. As already mentioned, O'Reilly Javascript: A complete guide is a great resource. If you need a reliable web resource, try the PPK website . You will also want to install Firebug - this is extremely useful for debugging. It also makes a great learning tool, you can open the console and play with any page you want. The DOM browser and tab completion make this very easy.
You can start by looking at Javascript separately, but simply enough so that you probably pick up everything you need just by looking at a few examples. Instead, I would suggest that you go back to the Javascript language as you progress. Learn about its prototyping of objects (and how it differs from the more traditional OOP classes that you may be used to). These concepts may take some time to “click” with some people, and you don’t need to know this when you start, so I would recommend painting it.
Please note that I have not mentioned AJAX or any frameworks yet - it will be much easier for you if you have basic knowledge in Javascript and DOM before you start looking for a framework. When it comes to manipulating the DOM, these platforms simply provide shortcuts and utility functions - if you don't know what it does behind the scenes, solving any problems can be very difficult.
I would also recommend using the infrastructure to handle AJAX complexities simply because (unlike manipulating the DOM and event processing) you have very few reasons to understand the complexities of XMLHttpRequest if you really don't want to. Let the environment take care of this and all browser compatibility issues.
Good luck