DevArticles has posted the first part of a new series today, one looking at the creation of a simple search engine with PHP and Ajax. It'll pull the data it needs from a backend database and display the results as transmitted through the Ajax connection.
In this particular article, though, they focus on the front-end of the system - creating the user interface, the look and feel of how it will function, and, finally, programming a behavioral layer to make the Ajax connection to the backend. It grabs the contents of the text field (in the form) directly and pushes it to a search.php on the backend.
Finally, they give you a full code listing for the entire setup so far to ensure you're up to speed.