Each state may have its own criteria for determining residency. If you are only in a state temporarily to attend school, then generally your state residency doesn't change.
If you need to prepare two state returns, prepare the nonresident return first. You may be able to claim a credit on your resident state return for any taxes paid to your nonresident state.
Also, some states have reciprocity agreements so that you normally don't have to prepare two returns if you only receive wages in the nonresident state. See this article for information on states with reciprocity agreements.
See also this TurboTax article and this one on multiple-state situations.
I agree with the other answer, you are still a resident of the state you were living in before going to school out-of-state. This is particularly true if you are still the dependent of parents living back in the old state.
Even though your residency doesn't change, you are still subject to state tax in the state your work in. For more specific info, identify the state you are from and the state you work/attend school in.
generally no. but if you have a DL for state A (former state of residency) most states give you a limited time to apply for a DL from your new state of residency. not updating the DL can cost you a nice fat ticket and possible other repercussions if ever stopped by the cops,