I live in New York and work in New Jersey. Do I have to pay on both tax returns or is there a credit I have to take?

First complete NJ return. Then report same income on NY and claim credit for taxes paid to NJ.
To your resident state, you must report your worldwide income for the year. Read: Your U.S. Tax Return: Working or Living in Two or More states (http://taxipay.blogspot.com/2008/06/working-in-two-or-more-states.html)