Open your web browser and go to the Qantas Manage Your Booking webpage. Type your booking number and last name in the fields on the right of the page and click "Go." Then, click "Cancel" on the next page and go through the options for your particular flight.
Call 1-800-227-4500, Qantas' phone number for telephone sales in the United States. Tell the agent your booking number and that you wish to cancel.
Contact any third-party agent you booked the flight through directly. Qantas can only cancel flights booked through its own website or telephone sales department.