How do you trust someone who has lied?
Simple, you choose to trust them again.
Now the tricky part is do they deserve the trust?
That is a question I would recommend bringing to your Inner Knowing.
And either way, I Highly recommend forgiving them. You are forgiving them for yourself, not because you condone what they did. For more information about forgiveness go here.
My favorite definition of insanity is doing the same thing over and over and expecting a different result.
Some people when they lie to you truly are sorry and will never do it again.
Others will do it again in the future no matter how much they say they are sorry and they won't. (and have probably done it in the past)
So how do you know who to trust again?
It is like one of my favorite lines in one of my favorite movies. The second matrix when the auricle answers Neo's question, how will I know if I can trust you? And she says that you'll just have to do what you've always done. You'll just have to make up your own dam mind.
What I make that mean is follow your inner knowing. Your inner knowing knows whether or not you should trust the person again.
Your inner knowing is your direct connection to your Higher self, spirit, soul, whatever you want to call it. This inner knowing knows everything.
When you follow this inner knowing, It will never lead you astray and help you know who to trust again, as well as who to trust in the first place. You always know, it is just a matter of listening.
For more information about your inner knowing go here