From the Airport, take S-Bahn S1 towards Wedel, and get off at Hamburg Central Station (Hauptbahnhof). Change across the platform to take S-Bahn S21 or S31, taking you to Dammtor (1 stop) or Sternschanze (2 stops).
From Dammtor station, it is just a few minutes walk to CCH or to the East Entrance of the Hamburg Fair site. From Sternschanze station, it is just a few minutes walk to the West Entrance or Central Entrance.
Travel time: travel by S-Bahn from the Airport to the Hamburg Fair or to the main entrance of CCH takes about 30 minutes (+ 10 minutes walk).