In order to apply for How to File Divorce Papers in New York you must first fulfill the residency criteria and then fill out the required forms, which include a Summons with Notice or Summons and Verified Complaint that lists the reasons for the divorce. Serve your spouse within 120 days after filing the paperwork with the Supreme Court. Submit a settlement agreement if both parties concur. The process will be completed when the judge issues a Judgment of Divorce following court approval.