The guaranteed way is the JFK air train to the A train to the PATH. There is 24/7 PATH train service from Manhattan to New Jersey. Google Maps is good for finding the best train station. PATH might be slow at night, but it will get you to Jersey City, Hoboken, Harrison, or Newark. Depending on where in NJ you need to go, you may also be able to find a NJ transit train from New York Penn Station or buses in/around the Port Authority Bus Terminal.