The PATH train system (http://www.panynj.gov/path/) runs from Manhattan to Hoboken, Jersey City and Newark.
NJ Transit (http://www.njtransit.com/) is a commuter network of trains, light rail and buses connecting communities throughout the entire state. It can be used for travel to Newark Liberty International Airport as well as Pennsylvania Station in New York City. Its website provides a user friendly method of planning your itinerary.
SEPTA (http://www.septa.org/) Regional Rail Lines connect Trenton and West Trenton with Philadelphia.
PATCO (http://www.ridepatco.org/) Operates a high speed train that connects several key points in downtown Philadelphia to many immediate southern New Jersey suburban towns.
There are also numerous taxi and limousine services that one can call for a pick-up, and a variety of county bus services that can take people to lesser-known spots in the state usually suburbs, parking lots, train stations, strip malls, apartment buildings, and/or small towns, depending on the county and the route.
Private bus companies, such as Suburban Transit, Martz Trailways and DeCamp, also work New Jersey and have routes in the state.
Some traffic oddities peculiar to New Jersey... Left turns are not permitted from many of the major divided highways in urban areas. Instead, exit ramps for left turns and U-Turns may follow intersections, providing opportunities to return to the desired intersection and make a permitted right turn. Also, many signals have a 'delayed' green light following a red, so keeping an eye on the traffic signal instead of observing oncoming traffic is essential. Traffic circles 'roundabouts' are quite common as well along major highways, and exits are not always clearly marked. Some toll bridges along the shore charge vehicles heading in one particular direction only, like toward New York State to the east and toward Delaware and Pennsylvania to the west.
