I'd definitely recommend to take the train, there is a direct ICE connection (high speed train) that goes every hour, journey time 1:30h. Even on German Autobahns you'll never be able to beat this by car, it would probably take you more than twice as long.
So, if you want to take the train: There is a bus connection from Hamburg Flughafen (airport) to Hamburg Hbf (main station). Take the ICE from there, get off at Berlin Spandau, from there it's only 10 minutes to the stadium by S-Bahn (urban railway).
Detailled information at the Bahn web site (German Rail):
http://www.bahn.de/app_internat.shtml
Regards,
Stefan