Train
You can catch Amtrak from NY Moynihan Penn Station (31st and 8th Ave) to the Hudson, NY station - usually on the Empire line. Ticket prices change depending on how early you purchase the tickets. I reccomend buying them at least a week in advance for the best price, but they can be bought even minutes before departure time. ($37-74 one way)
Travel Note
Cabs are difficult to come by and must be scheduled with plenty of time in advance.