There are many guys out there that will know I am not joking when I say what a hard job it is to win an ex-girlfriend back and is not something I would recommend anyone trying without first putting some thought into how they intend to do it. Unfortunately, our first reaction is to grovel or beg and although these may work sometimes, they are actually things you should try and avoid if possible, especially begging which should be avoided at all costs.
So learning how to get your ex back is not something you should try and do unless you are sure it is what you really want because, in many instances, it would be easier to just find a new girlfriend. Often though it is only after someone has lost their girlfriend that they realize how important that particular girl was to them and so cannot be replaced by just any other. It is times like that when winning an ex back is important and as being important, any troubles will be worth it provided you are successful.
So let us assume you have decided to get your girlfriend back which means she is the one you want and no other can replace her. This means that once you do get her back, you will not want to lose her again and so that is why begging is always a bad idea. When you began ex to return to you, if she does it is usually out of pity and so when that pity runs out, so does her renewed interest in you. Even if she did not return through pity, she still probably lost some respect for you since you had to resort to begging and that loss of respect will show later, perhaps once again driving a wedge between you.
Groveling although not really recommended either is probably something which will have to be done to some extent whatever tactics you try and so just try and keep the groveling to a minimum. Of course though, even if you do not see the reason for the breakup is your fault, you must apologize anyway. This brings us to the main important factor and that is: what was the reason why she broke up with you? This is something you must learn and have done so respect, even if you do not fully understand it as she thinks it makes sense and that is all that matters.
Hopefully the reason she finished with you is something you can easily fix, perhaps the way you dress or the attitude you show her but other things may be far more complex and so you may have to work on those, such as stop seeing other girls or perhaps even some of your other friends but if you want her back bad enough, it will be worth doing. Remember though you will have to show that you have changed and not just expect her to take your word for it.