From Hamburg Central Station (Hauptbahnhof), take S-Bahn line S21 (towards Elbgaustrasse). It is just one stop to Dammtor, and takes only two minutes. From Dammtor Station, it is only a 5-minute walk to Hamburg Messe (East entrance, Halls B4 / B5). Alternatively you may exit at Sternschanze which is only 5 minutes away from Central Entrance (Halls A1 and A4).
The Congress Center Hamburg is right next door to Dammtor InterCity rail station for the high-speed trains of German Rail and international rail connections.