As a general rule, with New York being the exception, a telecommuter is taxed in the state where they are actually working. So when you move, your employer should change your withholding to your new state of residence. During the year of your move, you will apportion your income between the two states, and file a part-year resident return in each state. After that, if your employer changes the withholding, you will only be filing a return in your new state of residence.
In the event that your employer does not change your withholding, that complicates your situation somewhat. You will have to file a non-resident return in your old state, indicating no income, to obtain a refund of withholding in that state. And you will have to file a resident return in your new state, on which you'll have to pay taxes in full. And of course, taxes in your new state will be due by April 15, while the refund from your old state will arrive when it arrives.
Nick K, EA