It is by public transportation VRN. One-way per adult is EUR 4,70, available at a ticket machine at the airport - or also online via the link bellow.
It is "Preisstufe 4".
Use the planer tool of VRN www.vgn.de/en/timetable/connection?Edition=en
You start at the airport by subway rail.cc/en/nuremberg/nuremberg-airport/l6692
. The system will show you two routes, one with change at "Nürnberg Hautbahnhof" (central station Nuremberg) rail.cc/en/nuremberg/nuremberg-central-railway-station/l147
and one with change at subway station "Nürnberg Rothenburger Str.". I personally would go for the first one. Then change to local train "S1". And again change in "Fürth Hbf" main station.
All in all it is not that complicate, you will see.
Hope this helps, Pete