By Bus, Under-/Overground
By Bus
Bus numbers 148, 174, 176, X76, 181, 182, 183, X83, 185, 186 all stop directly under or very close to the tower. The bus stop is usually called "Schloßstraße".
By Train
The U-Bahn stop "Schloßstr" is right underneath the tower. You can even access the tower from the platform!