More information is needed. What is the false and damaging thing that was said about you? Who was it said to? How did the false statement harm you? Were there any economic damages? Did the person who made the false statement know that it was false?
You start a lawsuit by filing either a summons and complaint or a summons with notice at the court and paying the filing fee unless you are indigent and can get a fee waiver. As for the rest of your question, you don't given enough information about the facts of your case to comment. There is a one year statute of limitations in NY for defemation that runs from the date of initial publication of the statement.
The above is for informational purposes only and not meant as legal advice.
It seems to me that there are too many pitfalls in defamation lawsuits for you to be proceeding on your own, especially when you indicate so little knowledge of how to go about this. There is also, of course, a concern as to whether the putative defendant has any assets, inasmuch as he is receiveing disability.
A lawsuit in defamation for someone who lives in Mount Vernon would ordinarily be brought in New York State Supreme Court, Westchester County. Defamation complaints must be carefully crafted and must state the particular words that were used, as well as other details concerning the defamation. Unless it fits within the limited scope of what is known as libel "per se," you must prove that you were damaged as a result of the defamation.
The problem is that defamation lawsuits can be quite expensive and that proceeding pro se as you apparently wish to do is fraught with many complications.
You should consult with a New York attorney who is experienced in this area of the law to determine how you should proceed.
Good luck to you.
Michael S. Haber is a New York attorney. As such, his responses to posted inquiries, such as the one above, are limited to his understanding of law in the jurisdiction in which he practices and not to any other jurisdiction. In addition, no response to any posted inquiry should be deemed to constitute legal advice, nor to constitute the existence of an attorney/client or other contractual or fiduciary relationship, inasmuch as legal advice can only be provided in circumstances in which the attorney is able to ask questions of the person seeking legal advice and to thus gather appropriate information.