Exit hahn on the right hand side and you will see buses depart directly from the side of the road in front of the terminal building.
I'd advise to not waste any time once you leave the plane and seek out the bus ASAP because it frequently leaves quite soon after you arrive and then you may have to wait around at the airport for an hour for the next one.
You have to buy your ticket before boarding at a Kiosk which is also outside beside the bus.
The kiosk was there when I flew to Hahn in March. The bus fare is 12 euro one way so if you can get a cheaper deal on the Ryanair flight then go for it! and the journey time is roughly 1 hour 45 minutes.
The bus will leave you behind the Frankfurt Hauptbahnhof main train station.