Everyone defines cheating differently, but an affair is usually a wake-up or break-up event in a relationship. Dissatisfaction is not the only reason that people cheat, some cheat simply because the opportunity presented itself. So while people don't necessarily go looking for someone else, they are seeking to be someone else. An important question to ask yourself if you are the one having the affair is 'Who do I get to be during the affair and what prevents me from being this in my primary relationship?'
How to start the healing process:
End and grieve the original vision you had for the relationship and define a new one. Grief tends to come in waves, some days you might feel like you are on top of things, only to be triggered emotionally again.
Focus appreciation on what is working and expand on that.
If you were the one who was cheated on - be aware of hanging onto the victim/martyr role as this results in feelings of powerlessness. The more insight you have into your own stuff, the better partner you can be.
Monitoring your partner's every move will not reduce your anxiety and it takes a lot of energy that may be better spent on improving the relationship. Frequent monitoring will often turn the relationship into a parent-child role and not one of two adults.
Working through an affair requires vulnerability from both partners.
Seek professional counselling to navigate the complexities of healing from a relationship. Communication needs to occur at the right time and in the correct way, counselling can assist with providing the safe space and tools to do this. Recovery from an affair can be a lengthy process.