We accept a U.S. Department of Defense Form DD-214 that indicates an honorable discharge.  If you don't have one I can tell you what other documents we accept as proof.
will I have to keep proving my service everytime I have to do business with the DMV?
After you receive the veteran designation, it will automatically be on all of your future DMV documents when you replace or renew.
what is the refund fee we get that I heard about?