Trust is the most fragile thing in the world. Once it has been bruised, it can heal but the healing is very slow and there will be scars.
The only way to regain trust is by behaving in a trustworthy manner. That means answering the other person's questions honestly and being willing to be accountable. If it's an affair, it means letting the other person have access to all passwords and cell phones.
If we're talking about an affair, only about 1/3 of couples can ever work past it. Among people who reach the point of divorce but reconcile, in five years 85% describe their marriages as happy. That drops to 30% if there has been an affair. And that's excluding the ones who divorce, so the percentage of relationships that reach the point they are again functional is even smaller than that. During my time as a marriage counselor, most of the post-affair couples that didn't divorce just reached a stalemate. Usually they agreed to remain legally married due to children and/or property, but their hearts were already divorced.
I reached the point in marriage counseling that I set very explicit behavioral expectations when there had been an affair. One of those was the offending party writes a letter to the other person, ending the relationship, and I mail the letter. I also insisted on complete accountability to the spouse. Accounting for whereabouts and not having any secret areas, such as cell phones or email accounts is also part of recovery. Basically, the injured spouse sets the rules for reconciliation and if the other party isn't willing then it's time for them to end it. That's really the only hope for complete reconciliation. Anything else is just a surrender to the situation.
You wouldn't believe the number of marriages which end up in "don't ask; don't tell." I even had a neighbor who would blow the horn and drive around the neighborhood to allow his wife's boyfriend time to get out of the house, if he was coming home early. I know that's extreme, but such arrangements aren't as uncommon as you might think. Basically, the couple just agrees to a sustainable level of misery.
If you're not referring to an affair, I've wasted a lot of type, haven't I? :) I don't know your situation, but I know a violation of trust is horrible. Best wishes to you and whomever.