Klagenfurt lies on both the South and the Tauern Railway Lines which give easy connections to Bruck/Mur & Vienna and also Villach and Salzburg. The journey time between Klagenfurt main railway station (Hauptbahnhof) and Klagenfurt Annabichl (nearest stop to the airport) is just 5 minutes. There is a train to Annabichl approximately every hour and it is just 5 minutes walk to the airport from the station at Annabichl.

Further information under www.oebb.at 

Timetable Information: http://fahrplan.oebb.at/bin/query.pl