You can have a veteran designation printed on your Nevada driver license or ID card as proof of service. It is free if you add it while renewing or doing another license transaction. On its own it costs $8.25 for a non-commercial license or ID card, or $12.25 for a commercial driver license.
Apply at any Nevada Department of Motor Vehicles office and ask for the veteran designation.
A copy of your DD214 or other discharge paperwork proving you received an honorable discharge.