Marc Plotz has written up a new tutorial for PHPBuilder.com introducing a simple way to get started combining PHP and Ajax with a "Google Suggest" type of example.

When you use Ajax with PHP, PHP does the calculations that it needs to do on the server and sends the result back to the page. You then use JavaScript to display these results in a predefined place. The demo application you will learn how to build in this article is a very simple Suggestion box, just like the one that Google made famous and thus ushered in the Ajax era.

The example (you can download it here) creates a basic form text field and the Javascript you'll need to make the callback to the waiting PHP script. It doesn't use any external libraries (like jQuery or Prototype) so be ready for bare-bones Javascript.