Mozilla's Getting Started
If you don't know anything about AJAX, I would recommend reading Mozilla's Getting Started Guide.  It has some good information about many of the different AJAX principals and will get you up to seed fast.

Saying Hello With AJAX (PHP)
This is a very simple, and very straight forward demonstration of AJAX with PHP.  It is very easy to understand and a good place to get started quickly.   A nice variation on the good ole "Hello World" we all love.