For your federal you will file one extension on Form 4868. Please see How do I file an IRS extension (Form 4868) in TurboTax Online?.
For the States it depends on the State. Please see Do I need to file an extension for my personal state taxes? If you need to file more than one state extension depends also on the military spouse's state of legal residence (home of record). If it is the same state as the state you live in then you will only have to file one extension (if your state requires it).
Please be aware that the service member always keeps his state of legal residence no matter where stationed and the income will be taxable in the state of legal residence unless military income is exempt by the state law. Please see What is my military state of residence? and Military Spouses and State Taxes for more details.
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