AMTRAK has a train stop in Northhampton and Greenfield! The train is called the Vermonter. It is a direct train to and from New York City, once a day.
In addition, the Amtrak runs to and from Springfield many times a day. Amtrak schedules and fares here: www.amtrak.com.
If you arrive in Springfield, continue to Travel by Bus. Caution: arrange your travel connections ahead of time. More buses from NYC terminate in Northampton or Amherst than come all the way to Greenfield.