Honolulu does provide an island-wide bus transportation system which serves the Daniel K. InouyeInternational Airport, for more detailed information for routes and price ranges you can visit the following website:
Roberts Hawaii Express Shuttle
This company provides an alternate, affordable transportation for passengers to their work, home, or a hotel. It is usually used for long-distance.
Of course, if passengers want to take a cab (taxi), their service is available at the airport’s property area.