For international guests we suggest you fly to Frankfurt/Main. There is a direct fast train (ICE) from Frankfurt Airport to Göttingen. You can buy tickets online at www.bahn.de. Select "Frankfurt Flughafen Fernbf" as your point of departure. If you buy the ticket online ahead of time, you need to bring the credit card that you used for your booking for identification on the train.
To get to Hann Münden it is best to take a local train from Kassel (either "Kassel Hbf" or "Kassel-Wilhelmshöhe") or Göttingen. The hotel's website says that it is within walking distance from the station, but it is probably easier to share a taxi to get there.
On Thursday evening we will leave for Göttingen (transport will be taken care of). In Göttingen the Leine-Hotel is booked till Sunday.