Train service from NYC to Pittsburgh departs from Pennsylvania Station in Manhattan. From JFK, take AirTrain to Jamaica Station, and then either the Long Island Rail Road or the "E" subway to Penn Station. There's only one direct train a day from Manhattan to Pittsburgh. It is Amtrak's "Pennsylvanian," which departs daily at 10:50 AM. There's also a connection available to Amtrak's "Capitol Limited," which departs from Washington, DC, to Pittsburgh, leaving Washington at 4:05 PM daily. You can check fares and availability at www.amtrak.com.
Have you looked into an inexpensive flight from JFK to PIT instead? Check fares at www.jetblue.com.
Train service from NYC to