Spouse relocated to another state. Spouse has worked and lived there all year, but employer still took out taxes for old state. This is not a temporary relocation. Other spouse plans on relocating. How to do State Taxes and get back taxes paid to wrong state?

You will have to file a tax return for the "wrong" state, documenting $0 earnings in that state, and hence get a complete refund of all taxes withheld. Be careful however - if the spouse that stayed behind has any income at all then that spouse does owe taxes in that old state, and you should not file jointly there. Specifics will depend on which states are involved.