TransferBus will charge you about �70 each way:
http://www.transferbus.net/tb/booking/step1
By public bus, you can take service 260, from in front of Terminal 1, to Lofer. Then take service 4012 to Kitzb�hel. If your German is good enough, there's an online timetable here:
http://www.postbus.at/de/Verbindung_suchen/
However, if I was doing it, I'd take the number 2 bus to Salzburg rail station. It runs every 10 minutes (or every 20 minutes on Sundays), with a 20 minute journey time. The fare is �1.80. From there, you can get a train, via Schwarzach-St.Veit (or occasionally direct), to Kitzb�hel. The journey time is around 2� hours, with a fare of �24.30 each way. The rail timetable is here:
http://fahrplan.oebb.at/bin/query.exe/en
This post is derived from these sources:
http://holiday.kitzbuehel.com/accommodations/
(Click 'How to get here')
http://engl.salzburg-airport.com/bus.html
Chris