AirTrain from your terminal to Jamaica Station; Long Island Rail Road from Jamaica to Penn Station New York (frequent service); NJ Transit from Penn Station to Princeton Junction (check www.njtransit.com for schedule).
As an alternative, you can consider the (more expensive) bus service offered by Olympic Airporter from JFK to Princeton. Details at www.olympicairporter.com. (Click on the link for Middlesex/Mercer County shuttle service.)
AirTrain from your terminal