By train: Take a train to Heidelberg Hauptbahnhof (Heidelberg Central Station), which is located about 3.5 kilometers from the palace. From there, you can either take a taxi or a bus to the palace. Bus lines 33 and 34 will take you directly to the palace, and the bus ride takes around 15 minutes.
By foot: It is also possible to walk to the palace from the city center, which takes about 20-30 minutes depending on your pace. From Bismarckplatz, one of the main squares in Heidelberg, walk along Hauptstraße (the pedestrian street), cross the old bridge, and then follow the signs to the palace.