Moving forward is an effort and struggle and in my experience, takes time.
It's a test in commitment. And there isn't truly a set standard by which to map out a "how-to." more than asking of your forgiveness, in my opinion, as humbling as that is, is in his owning up to not just the pain or discomfort this caused you, but also a time for him to recognise his vulnerabilities, accepting where/how/why he caught himself in this scenario.
It can lead to affair proofing and a deeper bond. It's important that he allows and accepts moments where you'll feel hurt still, provided you are committed to a desire to move past hurt.
It takes time and mutual effort.