You will be taxed on your wages both where they are earned and in your home state. However, your home state will give you credit (against their tax) for the taxes you paid to the nonresident state on the same income.
This is how the states avoid double taxation by allowing a state credit in your home state.
You will want to work on your nonresident state tax return first. You will then take a tax credit from your nonresident return on your resident state tax return.
