Honorably discharged veterans can have a veteran designation added to a New York driver licence, learner permit or non-driver photo ID card. There is no extra fee for the designation, though the normal transaction fees still apply.
Apply at any New York State Department of Motor Vehicles office, or by mail to License Production Bureau, New York State DMV, P.O. Box 2688 ESP, Albany, NY 12220-0668. For express mail, use License Production Bureau, New York State DMV, 6 Empire State Plaza, Room 424A, Albany, NY 12228.
Official documentation proving you received an honorable discharge; the DMV lists the accepted documents on its veteran designation page.