Ask at Ground Transportation counter about shuttle service and cost to Jersey City. You can also take public transportation; take Airtrain from terminal to Jamaica Station, transfer to either E subway (7.25 includes Airtrain) or LIRR ($8.50 Sunday "city ticket" and Airtrain) to Penn Station. Follow signs to PATH train (6th Ave. & 33rd St.) and take the blue/yellow PATH train (Journal Sq. via Hoboken-Sunday service) to Pavonia/Newport station.
Ask at Ground Transportation