Delaware adds points to your passing entrance exam score when you apply for state employment. Five points go to veterans discharged other than dishonorably, to Guard and Reserve members with at least 20 years who are still serving, to an unremarried surviving spouse, to the spouse of a member declared missing in action, a prisoner of war or forcibly detained for at least 90 days, and to the spouse of a veteran or member with a service-connected disability. Ten points go to honorably discharged veterans and reserve component members who have a service-connected disability. Separately, if you leave state employment to serve, you get seniority credit for up to three years of that service.
Claim the preference when you apply for a position through the Delaware state jobs system, and submit your supporting documents. You still have to meet all the eligibility requirements for the position.
Your DD214, plus your VA disability documentation, marriage certificate or casualty documentation depending on which preference you are claiming.