Determine the problem
You will need to understand what went wrong in the first place in order to be on your way to winning your ex back. You should understand the difference between determining the problem and heaping blames on yourself. Just be honest with yourself and accept your part of the blame.
Once you have determined the things that you messed up on, you should pluck up the courage to approach your ex with a heartfelt apology. A good apology accomplishes two things. The apology should clearly show what it is that you are apologizing for. Be very specific with your apology in order for it to have meaning. The apology should also show your readiness to make necessary changes in order to avoid the mistake in the future. An apology that does not accomplish these two goals will be limp.
You should not just pinpoint the thing that you are sorry about. You should demonstrate that you have spent time contemplating on the issue by giving a sound explanation on your reasons for being sorry. It will show that you have seriously considered what was bothering your ex.
If you can not see things clearly on your own, then do not be afraid to seek professional assistance.
Maintain your independence
The fact that you have accepted to adjust to your ex's point of view should not mean that you should always be the one to make compromises. You have your own individuality as well, which you should not sacrifice. There is need of give and take from both parties in order to have a healthy relationship.
Giving an apology is very important in winning back your ex. In order for it to be really effective, you need to be very honest.