I live in New Jersey and work in Delaware. I have Delaware state tax deducted from my paycheck. Do I file my taxes with the state of Delaware? Also, do I need to file with the state of New Jersey?

You file in both states - in DE as a non-resident and in NJ as a resident. You should first complete the DE form - they will tax you on earnings that you made in DE. Then you do your NJ taxes - they will tax you on your total income, but will give you a credit for the taxes you had to pay to DE. Result is you aren't taxed twice on yor DE wages.