How does military wife file state taxes?

It depends.  If she also is a Texas resident (she lived with you in Texas after your marriage or was a Texas resident when you married), she would not have to file a state return unless her Virginia job mistakenly withheld taxes.  (You can file the following form:  Form 763-S 2016 Virginia Special Nonresident Claim For Individual ..., and send it in to Virginia to get back any mistaken withholdings.  Because of Military Spouse Rules, she is not treated as a Virginia resident for tax purposes and is not taxed there.  She will want to inform her employer that she is not a Virginia resident.  Here is an FAQ which discusses this:  https://ttlc.intuit.com/replies/3302300.  

However, if she is not a Texas resident, she will file a Virginia resident return (if she has income) because she is considered a statutory resident of Virginia (See the Joe and Mary example in the FAQ above).  However, if she had no income earned in Virginia, then she will not need to file a Virginia return regardless of her residency.  (If you have an opportunity to get her TX residency for tax purposes, you may want to do this, since Texas has no state income tax).