If you are the nonresident spouse of a nonresident service member stationed in West Virginia, the income you earn in the state is exempt from West Virginia income tax. For tax purposes you can choose the service member’s residence or domicile, your own residence or domicile, or the service member’s permanent duty station.
There is nothing to apply for with the state up front. Tell your employer you are claiming the military spouse exemption so West Virginia tax is not withheld, and file a West Virginia return to recover any tax already withheld.
Your marriage certificate, the service member’s orders assigning them to West Virginia, and proof of the state you are claiming as your residence.