Summarize the following:
If you want to earn a girl's trust back, the very first thing you should do is to apologize sincerely about lying and hurting her. Whether you cheated on her, lied about spending a weekend with your friends in Vegas instead of at your grandmother's, or lied about a significant personal detail, it's inevitable that she's feeling hurt, confused, and like she doesn't know you anymore. Let her know that you understand how difficult you have made things for her, and that you deeply regret what you've done. Take FULL responsibility, show her you know you were wrong. She's not going to go for a half-hearted apology. It needs to be sincere and real.   Don't just say "I'm sorry" because you think it's the right thing to do -- say it because you mean it. If you're not sincere, she'll be able to tell. When you tell her you're sorry, look into her eyes, speak slowly, and face your body toward her so she knows she has all of your attention. You don't have to say that you're sorry a hundred times -- it's about quality, not quantity. Let her know that you understand all of the pain and suffering that you've caused her. If she doesn't think you understand her pain, she won't want to listen to you. Though you shouldn't make this all about you, let her know that you're feeling real pain because of your mistake. You don't have to go in too much graphic detail if you think it'll only hurt her more, but you should be honest about why you told the lie. Maybe you wanted to protect her, maybe you knew that the truth would hurt her, or maybe you were even embarrassed about the truth and wanted to cover it up. Whatever your reason, let her know why you did it -- this will show that you're already maturing and trying to reflect, and that you're not just going to move on without gaining some perspective.  Being honest about why you lied will make her feel like you're more likely to be honest in the future. Letting her know your motives will help her understand your perspective. Know when it's better not to be honest. If you just wanted to get with another girl because you were feeling bored or restless, then it's better to keep that to yourself. First, you have to make sure that it really won't happen again. If you doubt yourself or your future self and think you may make the same mistake, then spare the girl and work on fixing yourself before you get entangled with anyone else. If you don't think that you should be trusted, then why should anyone else disagree? Once you're certain that it won't happen again, then you should promise her that you're determined not to repeat your mistakes.  Be sincere when you tell her this. Don't make an empty promise. Let her know that you understand that actions speak louder than words, but make it clear that from now on, your actions will match your promises. Tell her that you're going to work on becoming a better, more complete person who wouldn't lie to her. Be open about the fact that you know that this is a process and that you won't change overnight, but let her know that you're willing to try to change for her. If you have a concrete plan for how you'll change, whether it's by keeping a journal, going to therapy, or just trying to be a more honest, more reflective person, then let her know what you'll do so you'll sound more sincere. Again, make it clear that you know this won't happen overnight, but that you want to put in the work because earning her trust back is the most important thing to you.

Summary:
Apologize. Be honest about why you lied. Promise it will never happen again -- and mean it. Promise you'll change.