The answer is not an easy one. First put yourself in their shoes or their situation, how would you feel if they did what you did to them, back to you. I am sure you wouldn't like it either. So it will take time to earn their trust back.
There are two kinds of people in this world:
1. There are poeple who give you trust at the beginning until you break that trust, and they take it away.
2. There are another people whom you HAVE to show them they can trust you first, before they give you trust.
I am like the number one example above. I usually give people the benefit of the doubt and give my trust to them until they break it. It works for me. But I know of some friends who they will not trust you until you have earned their trust. Usually these people are like that because at some point in their lives, they were dissapointed by someone, or somebody betrayed their trust to they've learned to shut the door on anyone when it comes to trust. Understably, it sucks when someone breaks your trust.
So, if you just broke someone's trust, then you are now dealing with a person like that number 2 example and now you have to work to get their trust back.
These are some tips or suggestions I can give you if you find yourself in the same sitation:
1. Give the person some time to heal their wound. They are feeling hurt right now, and the last person they want to talk to right now is YOU. you must be patient. Give it about two weeks. This will ensure that the person who you hurted, has time to reflect and think of what happened to them.
2. After they've had time to heal. Make an attempt to find out how they are doing. Usually they will tell you they want nothing to do with you, If so, than give it another week, but if you are successful in getting a conversation from them, they the first thing to do is to Apologize. Don't over aplogize. The more times you say you are sorry, the less chances you have that they will believe you, and this will make it worst because they don't trust you anyway. So you have to show you are truely sorry. Saying sorry its a BIG step in gaining someone's trust. But THE most important thing about saying you are sorry is to show that you are sorry. You are going to have to do some serious "kissing " to do. If you are not goog at kissing , you better start learning. Kissing is just a way to make the person feel important, specially women, they love attention, the more attention you give, the better chances you have into reconsiliation. The worst mistake you can make in the making-up process, is to make up with someone just to make yourself feel better. If you want to gain someone's trust, you must do it for them, and not for yourself.
3. Before Honor comes Humility (Proverbs 18:12) - This proverb is so true. I've met so many people that they want your trust without respect. If you geniunly want to have someone's trust or respect, you must humble you yourself. Pride will get you nowhere, specially with someone whom you've hurt.