I will be starting a job in New Jersey in 2 weeks . I don't know the rules for working in jersey while I live in New York. Due I pay taxes for both state & federal?? /

You will pay non-resident income tax to NJ, plus resident taxes for NY State (and NYC if you happen to live there). And yes, you pay federal taxes as well.

When you file your taxes next year you should complete the NJ non-resident tax form first, then when you do the NY State form you get a credit paid for taxes to NJ. Depending on your income level you may find that you owe a bit to NY State, since their tax rates are a bit higher than NJ's. That's one reason why most people who take a job in NJ move out of NY (not to mention the lower cost of living and savings in commuting time and expense).