OK I see they have built a new train station to serve the airport. BUT you need to be careful about words or you mislead out of towners! The Airtrain is the light rail that runs around the airport terminals and takes you out to the Newark Liberty Train station. At the train station you must change to a NJ Transit train.
http://www.panynj.gov/airtrainnewark/
Read the cost & tickets page CAREFULLY. You must buy a ticket that you will use on both the Airtrain AND on your NJT train.