You've been broken up with and all you can think about is taking steps to get your girl back. It is a difficult and trying time in anyone's life to deal with the feeling of being jilted by someone that you really care about and lingering in a state of uncertainty as to whether or not you will ever be back together.
Consider the reasons that the two of you broke up in the first place - is it possible to go back and fix things? If not, apologize for whatever it was that you did to wound your ex girlfriend so badly that she broke up with you. If it was a recurring thing, take the necessary steps in order to correct your behavior and make sure that every time you get a chance to see or talk to your ex girlfriend that you illustrate how much you have changed.
It is important that you don't become overbearing with your attention, but rather put in a little bit of time for honest, friendly communication without being a bother. When you are with her be sincere in all of your communication and do not try to push her into making a decision. Be respectful of her feelings and her wishes and devote plenty of genuine time to listening to her and responding in a thoughtful manner.
Try to remember the little things that you did to impress her or attract her when you first met but hadn't officially begun dating. Incorporate those things into your everyday interactions with your ex girlfriend- whether it is putting more time into your appearance or being more communicative and making an effort to engage her attention. These are helpful points of reference to consider when you begin taking steps to get your girl back.
As your platonic interactions progress, feel out her response. If she has been more and more interested in seeing and talking to you, perhaps she is beginning to feel the same way that you do. If she is consistently dodging your affections, then consider it a hint. Regardless of the outcome, if you care about the girl, make an effort to let her know that you are there for her in any context- whether you are friends or lovers. Nothing is impossible and in time as you both change and become different people it is always possible to get your ex girlfriend back.