Organizers form an LLC in New York by filing the Articles of Organization, pursuant to Section 203 of the New York Limited Liability Company Law, with the Department of State. Organizers prepare, sign and file the Articles of Organization that creates the LLC. Any person or business entity may be an organizer (it does not have to be a business lawyer or corporate attorney). Organizers may be, but need not be, a member of the LLC formed. You can obtain a basic Articles of Organization from the New York Department of State here (note, this form reflects only the basic requirements — Articles of Organization may include other provisions consistent with law).
Of course, if you have any questions on How to Form a Limited Liability Company in New York, it is best to discuss them with a New York Small Business Lawyer.