Train From NYC Penn Station:

The train is from New York Penn Station (Not Newark Penn Station) and takes about 25 minutes. 

At Penn Station get to the NJ Transit Trains area.  You have to find where to wait in NY Penn Station for the NJ Transit trains until the track number of the train to South Orange is called.  Tracks are only assigned 5 minutes before departure, then go downstairs to the track. 

Take the Morristown Line train on the New Jersey Transit to the train station SOUTH ORANGE. Do not get off at the Orange, East Orange, West Orange or the Mountain Station (which is in South Orange).

(The trains are called DIRECT trains meaning that you will not have to change trains; make sure that you do not get on a train that is not direct).  

Once at the South Orange Train Station you can go downstairs to the Starbucks.