Can someone tell me how to locate the actual naturalization papers, if they still exist, having found the card index?

I'm looking at the index card for a William Wray naturalized on Oct 11, 1866 by the Superior Court, New York county. His former nationality is also Queen of Gt. Britain (I though he had just misunderstood the question). If he is the right William Wray (I'm fairly sure he is because of the "marble cutter" occupation), then he's also Irish.

What information would such a 1866 New York naturalization record contain, and how would I go about getting it? I have very little experience with American records.