I think the other posters summed it up quite nicely on how to work on allowing yourself forgive, so I won't repeat that here.
Just to make it clear, no such betrayal has been done to me personally. However, I've been unfortunate enough to presence people who has been hurt by this kind of situation in the past, and I'm afraid that it will always continue in the future, since us humans are all imperfect to begin with.
I've seen good-natured people turn into savage and cruel beasts for something as terrible as a betrayal, and I just want to know how to console them in such a time, in a time when they think no one is no longer trust-worthy just because a person committed such a deed. I feel so uncomfortable being in the victim's presence because I no longer know if I'm talking to rational human being, or a human being who has been hurt badly by another.
While we're not always in control of what happens to us, we are in control of the ways in which we choose to respond. We alone hold the responsibility for our thoughts, emotions and actions. I don't think anyone else should feel like its their duty to minimize or do away with our pain.
That being said, depending on how close you are with this person and how much this person has revealed to you, I think all you can do is just offer silent support. Chances are, this person is very angry and hurt; encourage them to talk about it and be content to listen. Resist the urge to preach or talk about the dangers of this colouring their perspective for the rest of their time. When the wound is fresh, few people are open to talking about solutions or long-term thinking. They need to get the poison out of their system. Be their anti-venom by quietly letting them re-experience the good in the world. After they've had a chance to vent, next time invite them out to a soothing atmosphere, like a park, or take them to see a silly movie. Gradually change their mood and lead by example, but let them heal on their own time.
Sadly, I don't think you can ever know if an experience like this is going to scar them forever or teach them a valuable lesson they can learn from. It's up to them, not you, to deal with it.
As for forgiveness, I believe it is not a weakness. It takes strength of character to remain optimistic and open to the possibility to change (and, sadly, the possibility to be hurt again). Life is full of disappointments and most of them come from other people; if you clam up just because you're afraid of getting hurt again, you might protect yourself from hurt, yes, but you won't be living life to the fullest and welcoming opportunities of goodness and happiness.
Still, as much as I laud forgiveness as a virtue, I don't include 'forgetting' in the equation. If you forget something, you cannot learn from it and damn yourself to a future of repeating the same mistakes. The slate is never wiped clean, because it is a resume of our experiences and what we've learned from them.
In the meantime, good luck.