To regain the trust is hard. However anything is possible man.
What you need to do are:
1- trust yourself and others will trust you.
2- be better you. learn from mistakes. Show him/her that you have changed ..not telling him or her.
3- at the time being be more listener than talker.
4- show..show you have changed. makes her/him believe you have changed not telling or promising anymore.
5- Let's bygone be bygone. forgive and forget.