I'm not familiar with the company you're talking about, but shipping firearms to NY can be hit or miss sometimes. Some companies are familiar with the laws and will ship no problem, and other places are just trying to cover their asses and won't ship anything to NY, even if it's completely legal here. So you'd have to contact the individual company in regards to that.
If they're willing to send it to NY you're going to need an FFL to transfer it to you. These are either gun stores or other individuals who have this license and will recieve the shipment of the gun and transfer it to you for a fee. They run the background check and as long as everything goes okay they hand you the gun and send you one your way. If you're looking to get a long gun transfered one of the sponsors who has an ad at the top of the page is great. Volko Supply was friendly and easy to deal with, the only downside being they only do long guns, no hand guns.