Following a break up many people repeatedly question themselves to the point of philosophizing everything and thinking "What I can do to get my ex girlfriend back", and if things would have turned out differently if they had done things differently. Some may even begin writing apology letters and doing other stuff along this line of thought to fix their relationship.
The one key reason this just would not work because you do not know the actual reason for the break up. Woman tend to be emotional and at times, they themselves do not even know why they are feeling that way and what were the cause of the break up. It is futile to waste your energy to figuring out what went wrong.
The first thing you need to do is put aside the relationship for a while and do not think about "What can I do to get my ex girlfriend back". Hang out with your friends, make new friends, have fun and meet people. Make a change in your life and give yourself some time off. Staying away from your ex will work wonders.
With this strategy, you can make gradual changes within yourself and the way you view the subject of relationship. You will have a much better idea how to proceed with your ex in a few weeks. Whether it is getting back with her or moving on. If you decide to get back with her, it is time to figure out what is her feeling for you.
Now a more direct approach is needed to patch things with your girlfriend. The worst thing you can do is simply beg her to come back to you as it is not a good strategy. Take things cool towards your ex girlfriend.
Your ex would probably miss you badly by now if you had stayed away from her long enough. Play hard to get and how her you have moved on (do not over do it). This will arouse her to rethink things between the two of you.
If getting back together with your ex girlfriend is meant to be, things will become obvious from now. Do not fall into the trap of over analyzing the situation as it may prevent you from acting accordingly when you keep asking "What can I do to get my ex girlfriend back". Play cool, take things slowly and you will be alright.