All info about the locations

 The fastest way is to take either the  Airport Express (FEX) or one of the Regional trains (RE7, RB14)  or the S Bahn S9 from the train station which is conveniently located in the underground below the Terminal T1. All of them will bring you to the main station (Hauptbahnhof) in 40-60 minutes. In the main station you go down to the ground level and leave the station through the north exit (Europaplatz). On the other side of the street is the bus stop for the Bus M41 which is starting there in direction to U bahnhof Hermannplatz. Take the M41 and step out at "Anhalter Bahnhof" (4 stops or 7 Minutes). The Tempodrom is located on the other side of the sport area and is visible from there. The single trip with public transport to the Tempodrom and surroundings is 3,80€ (take ticket ABC!).