When arriving at Stavanger airport, get your money from an ATM in the airport.. No money exchange counter that I could find, so this is your only option if don't already have kroner.
Also, take the green bus (#9 route) into Stavanger town if you want to save money (29 kroner or roughly $6). The airport shuttle (Flybussen) runs more frequently and will get you there quicker (20 minutes as opposed to 40 minutes) but it will cost you about three times as much (85 kroner or $15). On Sundays, the #9 bus doesn't run, so the airport shuttle is your only option.