An attorney should assist you in preparing a deed, transfer tax forms for both NY state and NY city. Additionally, the person making the gift will need to file a gift tax return next year.
This depends on what County you live in. If you live outside NYC and the boroughs then you need a deed, a RPTL-5420 form which is for transfer tax. There is no tax but you still have to file it. You also have to fill out a TP-584 triplicate form. The most importaant form is the deed and must be properly prepared. You must follow the exact chain of title. The person giving it to you must use the same name on the deed, even with initials. In the City there are additional forms that must be filled out. I would contact an attorney to do this for you, it is not a great expense and this way you are sure to do it correctly.