1. Prove repentance: this will be a long drawn out process. You will not be able to just say you are sorry. You will have to be 100% honest with your partner about everything, even if they ask you questions like, "How is dinner?" All of the trust and past experiences you have had will mean nothing. You will not just be starting from zero as you would be if you had just met, but you will starting in the negative, and have to work really hard to bring yourself back into the positive. If you really want to make things right you will need to make proving your repentance your top priority.
2. Get therapy, counseling, etc.: this is a part of proving your repentance. However, your partner may not feel like they can work through this issue on their own. For many this is very scarring. So, let your partner know that you are willing to go in for marriage counseling, therapy, and any other type of thing they need you to do. This can really help you understand how much your actions hurt your partner, and the many things you can do to prove your repentance, and make your relationship work again.
3. Take steps like a little child: part of making things right after you have been unfaithful is doing every thing in steps. You are going to have to show how sorry you are, and learn again like a child. It will be a slow process, and you may feel as though you are being treated like a child, but that is because you have to be humble and submissive, and admit your wrong, and change your ways. You will have to tell them where you are, what you are doing, when you will be home, who you are going with, etc. They will be keeping tabs on you, and you will feel like you are in junior high again and have to check in every time your plans change, but if you don't, they may feel like you are trying to hide something from them.
4. Show love, don't buy it: one mistake many people make after being unfaithful is that they try to buy forgiveness. They shower their partner with lavish gifts, and they try to make things right by bribing them. You may not recognize this, but that is what your gifts say to your partner. Instead of working to show them your love through your actions, they feel like you want the easy pass-buy their love. While they may like the gifts, and happily receive them, they will do little to solve your problem and make things right again.
5. Never cheat again: while this is obvious, one of the only ways you can make things right again is to never cheat again. You can't even half cheat, meaning don't even talk on the phone with members of the opposite sex, let alone go out with, be alone with, flirt with, or more.

It will not be easy, but regaining a lost trust never is. However, if you want to make things right after you have been unfaithful, try the above.