Four distinctive plates honor eligible service members, veterans, retired service members and certain family members. Each plate has its own eligibility and documentation rules, and you apply in person at a DMV service center. The source page describes two of them in detail: the Disabled American Veteran plate and the Veterans plate.
Apply in person at a Washington, D.C. DMV service center with the proof of eligibility that the plate you want requires.
Proof of eligibility for the specific plate, which is usually your DD214, and your VA Benefit Summary Letter if you are claiming a disabled veteran registration fee exemption.