Have a look at jQuery, they have a function called fadeIn.
That is not what Google is using, but it is (probably) the simplest way you can recreate it.
Also, AJAX stands for Asynchronous JavaScript And XML, which is just another (friendlier) name for XMLHttpRequest. XMLHttpRequest is a way of sending data to and from the server without refreshing the entire page. When you view images in an album on Facebook and click on it, it loads the new image witohut refreshing the page. That is AJAX. Google (and jQuery's fadeIn) are what used to be called DHTML (Dynamic HTML), that is, clever JavaScript programming.