Waterfowl hunting at Montezuma is highly productive, highly esteemed, and is highly monitored. Hunting parties are limited so the hunting is great if you can get a reservation.
Hunting is permitted on Tuesdays, Thursdays, and Saturdays, by reservation first, and then fill-ins on the day of the hunt if it is not booked up, which I don't think happens very often. Check-in at the ranger station is required the morning of the hunt (I think an hour before shooting time but you have to look at the regs to be sure), and you are required to have a NYS waterfowl ID card in addition to your NYS small game tag and Federal duck stamp. Take a look at the *.pdf file on the website. It will tell you everything you need to know.
If you are in the area it is worth taking a drive through the refuge. There are a lot of birds there now and it is pretty fun.