Find out what he's doing on the computer. This may have its limits, and your man may have already taken steps to prevent you from doing this. Search for telltale evidence on his desktop, hard drive or other files. Remember that you are not doing this for your amusement but to get to the bottom of a potential duplicity. Look for the likes of porn, compromising photos of himself and/or those of other men or women, correspondences or classified listings.
Keep in touch with his social networks to have your finger on the pulse of his activities as well as any past, present or prospective girlfriends. These (re)sources may even alert you before you start entertaining suspicions.
Look for warning signs. If you are not the type to ransack your husband's or boyfriend's computer, take a more observational approach. See whether there are changes in his sexual habits, spending habits or involvement in couples-oriented activities. Notice when money seems to go unaccounted for or if he travels frequently. Be on the lookout for communications devices that are hidden or missing. Tune in to his body language to check for any inconsistencies in what he says and what his body says.
Notice patterns. Look for repeated instances of these signals in addition to the above warning signs. Act on them should there be a preponderance of these patterns.
Insist on an explanation. If you discover that the signals or warning signs recur or show up alongside others, confront your husband, boyfriend or partner about it and find out what is going on. Find out whether the secret life is still being played out and what the status of that relationship is. See what he intends to do about the situation, whether he will end that chapter of his life or if he has unresolved issues. Employ the services of a professional marital or couples therapist to explore the issues and feelings you are both having, and initiate the process of rebuilding the relationship should this be what you both ultimately decide to recommit to.