Newark Airport to West Point, using public transportation. Thank you to the parents who shared the information below.
There is a bus that goes directly between Grand Central and Newark Airport, called Newark Airport Express: http://coachusa1.reachlocal.net/olympia/ss.newarkairport.asp. The bus runs every 15 minutes during most of the day, takes about 50 minutes, and they have a special $5 fare with Military ID (normally $15). This option is much easier than trying to use the Penn Station / train to Newark airport approach.
The basic steps:
From Grand Central, trains run almost every hour northbound to Garrison or Peekskill via Metro North Line, approximately 80 minutes. Cost is approximately $10.
The train runs up the east side of the Hudson. To get across the Hudson via the Bear Mountain Bridge to West Point call a taxi (or a fellow cadet with a car willing to drive over and pick up). When "in season" a ferry for cadets runs from the Garrison station to West Point.
West Point is almost directly across the Hudson from the Garrison Train Station: http://mta.info/mnr/html/mnrmap.htm.