New Hampshire offers 12 distinctive military and veteran license plate designs honouring service members, veterans, retired service members and eligible family members. Each design has its own eligibility and documentation requirements, and samples are published on the DMV license plate example page.
Complete the Division of Motor Vehicles Application for Vanity Plates and apply at a DMV office or a town or city clerk's office that processes vehicle registrations, or mail it to NH Dept. of Safety, DMV - Registration Bureau, 23 Hazen Drive, Concord, NH 03305.
The proof of eligibility for the specific plate you want, which is usually your DD214, VA disability documentation, medal documentation or casualty paperwork.