The regulations are out for the 2011 Arizona Fall Draw that includes deer and desert bighorn sheep. Applications are due Tuesday, June 14th. There are no online applications; if you live out of state you must apply by mail and ensure your applications get to AZGFD by 7pm on the June 14th. If you live in Arizona, you can either mail your apps or drop them off at any AZGFD office.
Here's a link to the regulations: 2011 Arizona Fall Draw Regulations
If you're not sure where to apply, try contacting the following guys for some help:
Deer and Sheep: Southwest Hunting Adventures
Sheep: Colburn and Scott Outfitters
Deer: Arizona Strip Bucks