It would depend what they did and the circumstances involved. If they did something out of not knowing any better and seemed to later understand where they messed up (or any number of other circumstances), they may not have to do much to regain my trust (or at least regain it to a certain extent).
If they knew what they were doing and/or if it was out of having no respect for me or my feelings there'd be nothing they could do to regain my trust. I might decide to let whatever they did go, or even to forgive them for the most part. I would/could never, however, trust some people who did some kinds of things EVER again.
Most of the time, I think most betrayals of trust are not innocent, and not out of something innocent (like not knowing any better). Most, I think, are more likely to come from ego and/or from loyalty to someone/something other than the person betrayed.