Steps

1. Figure out their methods. Most spouses that are cheating online will go to chat rooms to meet members of the opposite sex. This is a very popular venue for cheating online. Find out which chat rooms they visit. You need to know which chat room they go into, and what method they use to get there.
2. Find another computer that is not in your house. Most usually a friend, or acquaintance will have a computer to utilize for this. Get to the chat room they go to at the same time they are known to be in it. Change your name so they cannot recognize it. You want to keep it a secret that you're there, otherwise you won't be able to catch them.
3. Flirt with your spouse under this assumed identity. Try to get his or her attention. Use all the flirting methods that you know to do so. Get him or her into a private conversation with you. Ask if he or she is married. If he or she says no then you, right there, have your evidence. If the answer is yes then continue to ask questions like “so does your husband (or wife) know that you come here?” Usually cheating spouses will deny that their spouses know. Then ask “So what brings you here? Looking for some fun on the side?” Once they have answered yes, then you have caught them cheating online.
4. Look for anything peculiar in their logs or documents. See if something strange stands out to you, like a file with a weird name to it, or even look in the folders that seem normal to you to see if you can find anything to prove that they are cheating online. Sometimes people that are cheating online will leave a little trail of evidence.
5. Don't install anything on their computer. This can easily be found out by antivirus programs, application errors (such as of the program you installed crashes, runs out of memory or even uses available hard drive space). Instead, look into capturing network traffic through your router or with programs such as Ettercap and Wireshark.