The cheapest way in. Nothing listed is quicker.
S-Bahn S1 and U-Bahn U4 to the HafenCity cruise terminal
S1U4 · S-Bahn Hamburg, HOCHBAHN, hvv tariffPickup, hours & luggage
Boards at. Station "Hamburg Airport (Flughafen)" beneath the terminals, on the S1 towards the Hauptbahnhof
One hvv ticket covers both trains: the Hamburg AB single, EUR 4.10 (child 6–14, EUR 1.50; under 6 free), or the Tagesticket Gruppe at EUR 16.40 for up to five. Both are 7% cheaper in the hvv app.
Luggage. A commuter train with standing room by the doors, then a metro train; busy at rush hour.
Hours. From the airport, every day; the U4 runs about every 10 minutes by day and every 20 in the evening. Nothing connects between 23:52 and 04:32.
