A couple things before we start: First, to make language simpler, I'll refer to the cheater as "he" and the betrayed spouse as "she." If you want to switch the genders, simply hold your computer up to a mirror. (Admit it, you almost did it, didn't you?) Also, I want to take children out of the equation. I don't do this because children are irrelevant—quite the opposite—but because, if they exist, I believe they are the most important consideration.
The jilted spouse should take of her kids (and any other obligations) in what she feels is the right way, and then take care of herself—and that's what I want to focus on. (The point of this post from an ethics perspective is that while most ethical systems are very clear about what not to do, they are often less clear about what you should do, especially for yourself.)
It will help to distinguish between two cases. In the first, the cheating spouse leaves the marriage, whether to be with the other woman or not, and the wife (now ex-wife) must deal with the aftermath. In the second, he stays in the marriage and the wife must consider her options, both within and without the marriage. I'll discuss the second case first, because if the wife does leave her husband, she'll be in a similar place as the wife who is left by her husband, so we can discuss these together at the end.
If the husband does not leave his wife, but instead stays in the marriage (and presumably ends the affair if it was still going when discovered), then the wife must decide whether to stay in the marriage. Since her husband did break the "forsaking all others" part of the weddings vows, in a sense she has no obligation to continue in the marriage (since he already violated it). Nonetheless, she may not feel that way; in my earlier post on divorce and adultery, I argued that from the potential cheater's point of view, divorce may not be the "honorable" option if he places a high value on the commitment or relationship itself.
Of course, this goes for the jilted spouse as well. If she places a high value on the relationship—on the "for better or for worse" part of the vows—then she may choose to stay married to the adulterer. Her task then becomes trying to deal with or get past the adultery, which we'll see is a common concern with all the cases we're considering, except in this case she must do so while married to the man who cheated on her (which I can only imagine will make reconciling herself with the adultery more difficult, and make therapy all but necessary).
If the wife feels that the marriage has been ruined, damaged beyond repair, or even if she simply has no desire to try to stay with a man who betrayed her trust, then she can leave her husband—certainly few would begrudge her this choice (absent children, remember). If shes does leave him, then she is in the same place as the woman whose husband leaves her, except for one important difference: the first woman chose to leave, whereas the second was left. Being left by the man who cheated on her only serves to compound the offense, including any harm to her self-esteem (already damaged by the affair). But if the woman leaves on her own initiative, then she has taken ownership of the situation; no longer is she letting the man steer their relationship, and she is taking charge of her own life.
But regardess of which spouse left first, the one cheated on has to deal with the aftermath, and I don't think there's any one best way to do this (though some of my fellow bloggers, especially those who are therapists, may disagree). Some may need to confront the memory (and perhaps even her ex-husband) directly in an attempt to achieve closure; some may need to forget and put the experience past them; and some may need to forgive as well as forget.
The general point is that she must do what is best for her; her only obligation at that point (ruling out children) is to herself. Not only in this common sense, this is also consistent with almost every school of ethVIS. Most versions of virtue ethVIS stress living a good, fulfilled life in action, which includes taking care of yourself as well as others. Kantian ethVIS (a variant of deontology) stresses duties of oneself alongside duties to others, particularly duties of self-respect and development. And utilitarianism, which asks every person to maximize total well-being, includes the person herself in that. It is not selfish (in the negative sense) to take care of yourself; it is only selfish if you ignore other obligations to do so.
So these ethical schools agree, wonderful—but what do they say to do? That's the hitch; none are very clear on that point. But I consider that to be a strength, not a weakness. While moral prohibitions are strict by their very nature—do not kill, do not steal, and so forth—moral "encouragements" are more general—help others and yourself. It's easy to say what not to do, but much harder to say what to do instead.
And this is because what to do instead depends on what is best for you: on your needs, your goals, your desires, your strengths and your faults. If you need to forget, then do what you need to do to put the experience behind you: connect with friends, meet new people, join a group, start or revisit a hobby, etc. If you need to forgive, then forgive (perhaps the help of a friend or therapist—or this post). If you need to move to a new town and start a new life, then do that. No one knows what will work for you better than you (maybe with the help of family, friends, or a therapist), certainly not moral philosophers, who can only offer generalities. And that has been a constant theme in all my posts dealing with ethVIS: it cannot provide firm answers, but rather offers you frameworks for using your judgment to find answers consistent with your own moral character and integrity.
So if you've been cheated on, and assuming you're taking care of those who depend on you (such as children, older relatives, etc.), then your primary obligation is to yourself, and I can't tell you how to do that (I just hope you do!). The only specific advice I would offer is to learn from the experience. By all means, don't dwell on it, don't ruminate, and don't beat yourself up. But after some time has passed, and some of the pain has healed, take a moment to reflect, either by yourself or with the help of a friend, and see what you can take from the past to make your future better, and come out of it a better person.