I am curious how taxes are handled if I live in NJ and work in NY

You need to file a state return for NJ and a non resident state return for NY.

You fill out the NY non-resident form first - on that you report all your income, and pay tax on the portion that is NY source at NY's rates (around 6.5%). Then you compute your NJ tax, including all your income, and you take a credit for taxes paid to other jurisdictions. Result is that because NY's rates are higher than NJ's, you will probably not owe NJ any tax at all unless you have significant non-NY sources of income (such as a spouse who works in NJ, dividends, interest, capital gains, etc).

NJ is your tax home and NY is where you earned the income. You must report this on both the State returns.
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)