Hi!
From the Airport you must take a bus to "Lückbeck ZOB", this is p.e. Bus 6 (direction: Hamburger Strasse)!
From there, you must walk 5 minutes to get to the station and there you take the train to hamburg! This will take you 50 minutes.
In Hamburg, you have two opportunities, you can drive to itzehoe via Elmshorn, or you can take the "SBahn" and drive from Hamburg HBF to Hamburg Altona, where the train to itzehoe starts... the whole trip will take you roundabout 3,5 hours...