Personal relationships almost never run absolutely smooth at all times, because as human beings none of us are faultless, so when a break up occurs it is safe to say that there was mistakes made on both sides.
However if you need to get your ex back you must look at some important facts.
It is so very important to review your relationship at this point.
Were there constant disagreements? How minor were the mistakes and disagreements? Be very honest with yourself, did you ever silently wish you were out of it? The big question here is "do I really want her/him back?" The answer to that must be very clear in your mind.
I may take a little time for it to become clear.
For your part in the break up you need to take full responsibility for fixing it and making amends.
A simple apology is a great start if you mean it and say it with true meaning, but it really is going to take a lot more than that if you wish to get your ex back into a meaningful relationship.
You must deal with you emotion about how you feel.
If you allow yourself to believe that your ex will never forgive you, you will not be able to make any progress at all.
As hard as it maybe, you should approach the task of getting you ex back with a positive attitude.
You also need to fully understand what went wrong before you have any chance of fixing it.
If you need to get your ex back be fully committed to it.
If you are prepared to lose the battle and win the war you will have a big chance of success.
Take full responsibility and ask for forgiveness and mean it may be all that it takes.
Above all of that there are three most important things you must do, communicate, communicate, and communicate.
Listen, be attentive and care more for your ex than you do about your own feelings or desires.
Mean what you say especially when apologizing and asking for forgiveness.