If you want to know how to win the trust back, first learn to agree that you have made a mistake. If you still think that you've done nothing wrong, then you need help or your girlfriend really didn't matter to you that much in the first place. Relationships are complicated and they require work. Sometimes the feeling of helplessness is all that you can feel, but that doesn't mean that you give up and do something stupid that screws up everything. Moreover, relationship issues are tough but always remember infidelity is unacceptable in any case.
Mostly, men are emotionally unstable and sometimes have no control over their needs. The moment we have an argument or a fight with our partner, the next second we are eying someone else. Most men would not agree to this but it's true. Right now what you did to break her trust can't be reversed or changed as it has been already done. But what one can do in order to get her trust back is to make sure you imbibe the quality of empathy in you. Just imagine how would you feel if she had cheated on you or if she slept with someone else, you would probably murder her for doing that. You would even not like to speak with her ever again. So if you can get angry just imagining something that hasn't even happened, you should think about how she must have felt for the same. She loved you and you broke everything you as a couple shared.
You cheated on her so stop living in the dream that says women are full of forgiveness. They aren't and they never will be. For you it's a mistake but for her it's a period when she would experience many emotions at the same time. Hurt, betrayal, tears, anger, and possibly leaving you for better. If your girlfriend has left you because of your drunken mistake don't think that your world is over. You need to pick up the broken pieces and start thinking of ways to get her trust back.
First of all, ask yourself do you really want her back or this drunken mistake was something that you wanted to do. Your girlfriend obviously has left you and moved to her folks. So, take this time alone and think of your true feelings about her. Do you still love her? Because if you do then you can try to reconcile. You have broken her heart and she is going to treat you like some random person and bear with it. You may not be her prince charming anymore, not after what you did. Even if your girlfriend forgives you her folks may poison her mind by saying that you would do it again. She would probably listen to their advice for which she can't be blamed either after what you did. Remember she would only give you a second chance if she believes that you won't cheat again.
Re-building her trust would now depend wholly on you as you had broken it. Women are emotional. For them love and hate are two sentiments which they live in extreme. Here are some tips that might help you out.
Don't Try to Communicate with Her
Lots of men try this desperate attempt and all of them have failed. After a break up a person needs space and you have to give it to them. If you keep calling your girlfriend and keep texting her you are driving her away from you, which is something that she is not looking for. If you give her space, she might actually miss you and want to reach out to you.
Don't Follow Her
This is never a good idea. Everyone has tried it and it never works. Even Chandler in FRIENDS tried stalking Janice and it didn't work out well. Some guys even hire a detective and trust me she would find out in someway or the other and you may lose her for good.
Don't Try to Talk to Her Friends
This is never helpful. We all know that girls talk and they talk a lot. If you keep in touch with her friends and keep asking about her, they are going to tell her and it's going to make her more angry. The best thing to do is keep moving on with your life and let her friends see how you have been doing. Her friends would tell her about the new you and this is sure to work out in a positive way.
On a conclusive note, give her some space and leave her alone. Time is a great healer. So, one can try out the aforementioned tips that may prove useful. Moreover, if she gives you a second chance, make sure that you never repeat the mistake again. Start working on it and always keep the quality of empathy in you.