I am a NY state resident and moved to NC in Nov 08 to do my paid college 6 month internship. I have earnings from NYS and NC as well as state withholding from both states. I'm not sure on how to do my state income tax, part-year resindent or non-resident of NC?

Any income earned while present in a state must be reported to that state.
To your resident state, you must declare your worldwide income. If any income was earned in other state, you will claim credit from your resident state.
Read Your U.S. Tax Return: Working or Living in Two or More states

Unless you intend to stay in North Carolina, you should file as a non-resident when you file the NC tax return.

On your NY state return, you should claim the NC taxes paid as a credit on your NY state tax return. That way, you avoid the double taxation.

Though not required, it is normally a good idea to attach a copy of your NC state tax return when you file your NY state tax return.