I have found a flight from Frankfurt International airport (FRA), but from my city only Ryanair flies to Frankfurt-Hahn (HHN). The problem is that one airport is 114 km from the other. What's the cheapest way to go from one to the other? (I have time)
Personally I would suggest looking for a different routing - as you've discovered Frankfurt-Hahn airport is a very long distance away from both Frankfurt itself, as well as from Frankfurt am Main airport.
If you do decide to go ahead with this connection, there is a bus service that runs between the two airports, run by BOHR. Travel time is 90 minutes, and cost is currently 14 Euro per person each way.