http://www.alaskaair.com/mileageplan/faqs/credit.asp

For Partner Activity - Air, Car, or Hotel
Mileage credit may be requested by providing the following:

For air travel - a copy of the passenger receipt and at least one boarding pass.
For hotels - a copy of the hotel folio or bill.
For car rentals - a copy of the car rental agreement - (Avis, Hertz and Thrifty require a flight in conjunction with your rental for mileage credit).
Copies should be mailed or faxed directly to the Mileage Plan. Be sure to include your name and Mileage Plan account number with all correspondence.

Mileage Plan
P.O. Box 24948
Seattle, WA 98124-0948

Fax Service: 206-433-3477 (24 hours)