Hi, Steve! I'm no expert, but in NYS, your 'new toy' should qualify as a light duty trailer with an unladen weight under 999 lbs. If you really did 'inherit' it from a friend or family member, you're exempt from sales tax. You should be able to register the trailer as a homebuilt just by going to the DMV with some info that you can find on the website:
http://www.nydmv.state.ny.us/register.htm
I don't know if you need a bill of sale, but I do know that registrations of very old trailers that have been out of the DMV system for awhile are usually issued a non-transferable registration so that they can give you the plates, and then DMV converts that to a transferable registration within about 30 days. I just registered a 1980 Sunspot that had been off the DMV books for the last decade, using a dealer's bill of sale. If you don't have that, it might be more complicated unless you could prove that it was a gift.
Where in the Finger Lakes is your new toy 'summering?'
I'm just west of Syracuse on the shores of lovely Onondaga Lake
...about 20 minutes from Oneida Lake, an hour from Seneca and Cayuga Lake, and maybe an hour and a half from Lake Ontario. And next weekend is supposed to be a good as this weekend was, so you should have a lovely visit to its summer place.