Suing a cheating spouse typically falls under the domain of family law and may involve different legal actions depending on the circumstances and your goals. Here are some steps to consider:

1. Consult a Lawyer: The first step is to seek legal advice from a family law attorney who specializes in divorce and infidelity cases. They can guide you through the process and explain your options.
2. Determine the Grounds for Lawsuit: In some jurisdictions, you may have the option to sue for "alienation of affection" or "criminal conversation," which are claims against a third party involved in the affair. Your attorney can clarify if these apply in your case.
3. Gather Evidence: Collect any evidence of cheating, such as text messages, emails, photographs, or witness statements. This evidence will be crucial in supporting your claims.
4. File for Divorce: If you choose to end the marriage, you may need to file for divorce as part of the process. Infidelity can impact divorce settlements, custody arrangements, and alimony decisions.
5. Consider Mediation: Before pursuing litigation, consider mediation as a way to resolve issues amicably. It can be a less confrontational and potentially less expensive option.
6. Proceed with Legal Action: If you decide to move forward with a lawsuit against your spouse or the third party, your attorney will help you file the necessary paperwork and represent you in court.
7. Prepare for Court: If your case goes to court, be ready to present your evidence and arguments effectively. Your attorney will guide you through this process.
8. Understand the Potential Outcomes: Be aware that suing for infidelity can be emotionally taxing and may not always lead to the desired outcomes. Discuss potential consequences and expectations with your lawyer.

Remember that legal processes can vary significantly depending on your location, so it's crucial to consult with a qualified attorney who can provide guidance specific to your situation.