Not the easiest way... I live in this area and most people go to Airport Frankfurt Hahn by car - as it is more or less in the nowhere - an old military airbase.
Even it is called "Frankfurt", it is not close to Frankfurt and not connected to the railway network.
- book a bus ticket from Frankfurt Hahn to Ludwigshafen at flibco. com for EUR 20
- then continue by train from "Ludwigshafen (Rhein), Hauptbahnhof" to "Primasens, Hauptbahnhof". Schedules and ticket (EUR 10,50) available at vrn.de or at the station at a ticket machine.
From where do you want to fly to Frankfurt Hahn? Maybe there are better options available.