PHPBuilder has posted an excerpt from an Apress book today - "Beginning Ajax with PHP: From Novice to Professional". It's from the third chapter that introduces the PHP and Ajax combination.
The article's pretty light on the code, but it does give a full example of showing and hiding dynamic content pulled from a backend PHP script (calendar information). Outside of that they just discuss general topics like "Why PHP and Ajax?" and the difference between client-side and server-side processing.