$_SERVER["HTTP_USER_AGENT"]
is the PHP variable that holds the browser information. A easy way to see this and other variables is to create a file and put this code in it.
<?php
phpinfo();
?>
Runs this page and you'll see a section called 'PHP Variables'. This will give you an idea of the superglobals and what values they hold.
Now how you go about parsing this variables contents to get what browser it is I dont have an easy way, but it could be done fairly simple if you knew the values of the different browsers. Here are two examples:
This is a Mozilla 1.5 value:
$_SERVER["HTTP_USER_AGENT"] Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.5) Gecko/20031007
This is a IE 6 value:
$_SERVER["HTTP_USER_AGENT"] Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1; .NET CLR 1.1.4322; .NET CLR 1.0.3705)
I bet somebody has a list of values for different browsers. This should help enough to get you looking in the right direction.