Face it head on.
Cheating can be a difficult thing to confront your partner with. After all, you want to trust them. If you suspect your partner of cheating, you have to confront them honestly and directly. You will only be able to move on from the issue of cheating once you've determined the level of unfaithfulness your partner has committed.
Don't try to "get back" at your partner by embarrassing them or cheating, or having an emotional affair.
You have every right to be angry and hurt, but doing something to retaliate for your partner's infidelity will not help you feel any better in the long run. Don't commit an act you'll one day regret.
Forgiving your partner for cheating can be the most difficult thing you'll ever do. But it is key to moving on both in the relationship and from it. Remember, though, once you forgive your partner, you're not allowed to keep bringing up the issue. Live with the belief that your partner is working on the relationship as hard as you are. Bringing up the past for no good reason (even when you're angry and hurt) will only serve to hinder you both from moving forward.
Cheating is wrong, let's be clear about that. Sometimes one partner's affairs may have more to do with their own character flaws than with issues in the relationship. Some people are cheaters, plain and simple. But if this is not the case in your relationship, you need to come to terms with underlying issues between the two of you. Seek professional help if you need to. Without doing this step, you will likely continue with a relationship that is rocky at best.
Get back to the roots of why you fell in love. Go on dates again! Participate in activities that help you be a team. Surround yourself with friends who support your relationship.
A promise that your partner will end the affair is not the same as truly ending it. Be clear on the fact that in order to continue with the relationship, your partner must have already ended the affair and will not engage in another one. No compromises on this one.