If you are coming from New York City you can take the Metro North Hudson Line to Poughkeepsie from Grand Central Station. The train ride is about two hours. Trains on Saturdays depart Grand Central Station approximately every hour and approximately every thirty minutes on Fridays. 
Keep in mind that if you are not staying the night in Poughkeepsie after the wedding, the last train back to Grand Central Station leaves Poughkeepsie slightly before midnight with the next train leaving around 4:30am.

If you are flying in from out of state it may be best to rent a car. However, there are a plethora of transportation options locally for those who would prefer not to drive including taxi services, Uber, and Lyft.

Located in Rye Brook, New York this airport is one hour away from Poughkeepsie

Located in Queens, New York this airport is one hour and forty-five minutes away from Poughkeepsie

Located in Newark, New Jersey this airport is one hour and fifty minutes away from Poughkeepsie

Located in Queens, New York this airport is two hours away from Poughkeepsie