Trusting the Untrustworthy
When trust is broken in a relationship, and the people in the relationship decide to stay together, often people's first question is "how do we rebuild trust?" This is a great question for the person who broke the trust to ask. It shows an understanding that trust has been destroyed and a willingness to do the work to build it back up. This is especially important in poly relationships, which tend to involve more freedom than mono relationships, and thus require a higher degree of trust.
The problem is that I've heard this more often from the party who was betrayed. The party whose trust was broken should not be attempting to rebuild their trust. When you trust someone who then betrays that trust, the only reasonable conclusion is that you were wrong to trust that person in the first place. You misjudged that person's trustworthiness. Your goal moving forward should be to accurately judge the other person's trustworthiness, which is necessarily less than you previously believed it to be.
I read a post on r/polyamory today by a woman whose long-term boyfriend lied to her about condom use (an issue that my household has some experience with), and then went ahead and lied to her again. Her questions was "What can I to get back ability to trust him again?"
Don't trust him. You shouldn't have trusted him before. The fact that you were surprised by his behavior shows that you misjudged his trustworthiness. He's willing to lie to you in order to get what he wants or avoid conflict. Therefore, you should not trust him to tell you the truth when telling the truth could cause conflict or prevent him from getting what he wants. Your goal should not be to rebuild your trust to where it was before - that's putting yourself in the same position. The only reasonable goal is to accurately assess his trustworthiness and conduct yourself accordingly.
Sadly, I see this sort of thing all the time. My theory is that it's a kind of motivated reasoning that looks something like this:
(1) good relationships require trust (2) I want this to be a good relationship (3) Therefore I must learn to trust this person
This sort of reasoning is, of course, completely backward. A person isn't worthy of your trust just because you want them to be. A person is trustworthy because they tell the truth, even when it's unpleasant, even when it causes conflict, and even when it could result in unwanted consequences. Unless you have specific, articulable examples of a person doing this, your trust is nothing more than blind faith.