If you truly know why this break up happened, then you could proceed forward with a plan.
If you are at fault in causing this, are you in a position to correct whatever it was that you did or did not do? If you are not willing to make up to your ex for whatever it was, then you would most likely be wasting your time.
If your girlfriend is to blame, are you willing to take her back without her making amends or should she fix whatever caused the break up? If you would take her back without taking care of the issues that caused your break up, the chance of it happening again is great.
How well do the two of you communicate with each other? Communication skills are important in talking to each other about getting back together.
Let your ex have her say about your relationship.
Giving her a chance to voice her opinions may bring issues you did not know about out to the front.
Avoid arguing with her about why the break up happened or whose fault it was.
Now is the time to move past that and start new, do not bring up anything that will re-ignite anger in your ex at a time when you are trying to make things better.