Probably by train, approx. $25: go to the Metro North/NJ Transit station at Salisbury Mills-Cornwall (southwest of New Windsor on the other side of the Thruway) and take the Port Jervis line train to Secaucus Jct, go to the station upper level and take any NJ Transit train to Penn Station ($14), transfer to LIRR ($5.75) or E subway ($2.25) to Jamaica and take AirTrain ($5) from there to terminals.
Probably by train, approx.