If you travel by car, you will probably arrive via the A7, which is Germany's longest highway. In this case you should use gateway "Schnelsen Nord".
In all other cases you should use the ring-roads at the end of the highways. There will be signs that lead you reliably to the airport.
Please click on "city map" to navigate savely in Hamburg. If you travel by train, then select "city trains" from the following links.