Theres a bus from the Port Authority that goes there, not sure of the number or anything like that. Or you can take a train to Newark and take a cab.
There is actually a Newark Airport train station, but it costs $30.00 total from Penn Station, which includes the Air Train, then you still have to pay bus or cab fare.
You could probably also take the train one stop further to Elizabeth, but then your backtracking at that point by cab.