If you are going to use AJAX I would recommend using jQuery as well. This greatly simplifies the process, is tested cross-browser and has many easy to use wrapper functions.
Its really as easy as creating a PHP page called hello.php
<?php
echo "Hello World";
?>
Then in your main page you will need to grab the jQuery library and hook it up to the document ready event.
<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.4.4/jquery.min.js"></script>
<script type="text/javascript">
$(function(){
$.get("hello.php", function(data){
alert(data);
});
});
</script>
This in essence is the simplest AJAX hello world tutorial I know 🙂