In New York, an uncontested divorce can be a straightforward and cost-effective way to end a marriage when both spouses agree on all key issues. Here's a step-by-step guide on how to navigate the process:

Meet the Residency Requirements: To file for divorce in New York, either you or your spouse must have lived in the state continuously for at least two years before starting the divorce process. There are exceptions to this rule, such as if the grounds for divorce occurred in New York and either you or your spouse have lived in New York for at least one year prior to filing.
Determine Grounds for Divorce: New York allows for both fault-based and no-fault grounds for divorce. For an uncontested divorce, the most common ground is the no-fault option, which means the marriage has been irretrievably broken for at least six months. Both parties must agree to this ground.
Reach Agreement on Key Issues: In an uncontested divorce, you and your spouse must agree on all major issues, including division of assets and debts, child custody and visitation, child support, and spousal support (alimony). It's advisable to work with a mediator or attorneys to ensure that your agreement is fair and legally sound.
Prepare and Sign the Necessary Documents: You'll need to prepare and sign several legal documents, including a Summons with Notice or a Summons and Verified Complaint, which initiates the divorce process. Other forms may include a Statement of Net Worth, which details your financial situation, and a Settlement Agreement, which outlines the terms of your divorce agreement.
File the Forms with the Court: Once the documents are prepared and signed, they must be filed with the appropriate court in your county. 
Serve the Papers: After filing, you must serve copies of the divorce papers on your spouse. This can be done through personal service by a process server or someone over the age of 18 who is not a party to the action. Your spouse will then have a specified time to respond.
Complete the Divorce Judgment: If your spouse agrees to the divorce and the terms of the settlement, you can submit a proposed divorce judgment to the court for approval. This document finalizes the divorce and incorporates your settlement agreement.
Attend the Court Hearing (if required): In some cases, you may need to appear before a judge to finalize the divorce. If everything is in order, the judge will sign the divorce judgment, and your divorce will be granted.
Obtain the Final Divorce Decree: After the judgment is signed, you'll receive a copy of the final divorce decree, officially ending your marriage.
Comply with Post-Divorce Obligations: Once the divorce is final, both parties must comply with any obligations outlined in the settlement agreement, such as making support payments or transferring assets.
Keep in mind that while an uncontested divorce can be simpler and faster than a contested divorce, it's still a legal process that requires careful consideration and attention to detail. It's always advisable to consult with a qualified attorney to ensure that your rights are protected and that the terms of your divorce agreement are fair and enforceable.