We have just been to Girona airport. I found that there are lots of private taxis who will take you without prior booking. The Catalan bus company http://www.Sarfa.Com web site is very usefull and so is the trains which is http://www.renfe.es. You will need to get a bus/taxi to the nearest train station.

You can arrange a private un official taxi, however theses vehicles are not allowed on the airport site and you will have to trace them in the public car park.