You need to look at:
$_SERVER['HTTP_USER_AGENT']
That will contain the User-Agent string for the browser. Beware that almost all browsers claim to be "Mozilla" for compatibility reasons - you need to look for specific text for each browser within that header, eg. "MSIE" for Internet Explorer.
Some examples:
My Firefox calls itself Mozilla/5.0 (Windows; U; Windows NT 5.1; en-GB; rv:1.9.0.11) Gecko/2009060215 Firefox/3.0.11 (.NET CLR 4.0.20506)
My IE7 calls itself Mozilla/4.0 (compatible; MSIE 7.0; Windows NT 5.1; GTB6; User-agent: Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1; SV1; http://bsalsa.com) ; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729; .NET CLR 4.0.20506)
Note all the trickery in the IE one, eg. claiming to be multiple versions.