You get free entry to a New Jersey State Park or Forest during an event held by a veterans organization, and the organization pays no facility fee to use a state park or forest for the event.
There is nothing to apply for as an individual. Tell the park staff you are attending the veterans organization event. The organization should arrange the facility use with the Division of Parks and Forestry in advance.
Proof of your veteran status, such as your DD214 or a driver licence with the veteran designation, and details of the event you are attending.