Bad Ems is located in the beautiful Lahn valley, about 20 minutes from Koblenz where the rivers Rhine and Mosel meet.
From Frankfurt train direction "Limburg", change in Limburg to train direction "Koblenz". Travel time between 1h22 and 2h11 depending on your connection. It is a very pretty train ride!
By plane: Frankfurt International Airport or Frankfurt Hahn
By car from Frankfurt International Airport:
By train from Frankfurt International Airport: take the subway to Frankfurt central station (Hauptbahnhof), from there see above.
By car from Frankfurt-Hahn Airport (inexpensive car hire):
There are also regular buses from Frankfurt-Hahn to Koblenz: http://ma.rmv-bus.de/Hahn/busfahrplan.htm
Bad Ems is a 15 minute pretty train journey from Koblenz.