How are the taxes figured whe one lives in New york city while working in New Jersey for a NJ firm

how are the taxes figured whe one lives in New york city while working in New Jersey for a NJ firm
Employer required to withhold and you are required to file NJ tax return for earned income. NY will allow a credit for NJ tax paid.

Delite has it right, but since NY and NYC tax rates are a LOT higher than NJ, you will need to have income taxes for BOTH NY state and NYC withheld as well.