The page requires registration which is probably going to stop most people looking any further, by the way.
Since I can't see the page (sorry, but I'm not registering), I will assume you want the same functionality as the Google search engine? I.e. it will bring up search results matching the words you're typing in before actually performing any search.
The following code is an AJAX request which will open a PHP file and have the results returned:
var xmlhttp = "";
// IE7+, Firefox, Chrome, Opera, Safari.
xmlhttp = new XMLHttpRequest();
// IE6, IE5.
xmlhttp = new ActiveXObject("Microsoft.XMLHTTP");
xmlhttp.onreadystatechange = function()
if(xmlhttp.readyState == 4 && xmlhttp.status == 200)
// Handle HTTP response here.
xmlhttp.open("GET", "some_page.php", true);
I've written an article on how this works if you're interested. It's "how to check username availability with AJAX", but all the code you need is available in the tutorial. You'll just have to set up your PHP file to echo out the results of your given database table(s).