Getting back your ex girlfriend isn't going to be an easy task...anybody who says it is easy has never had to do it. It takes a lot of time and effort, and there'll be times when you wonder if it's even worth all the trouble to get back somebody who hurt you so badly...but if you remember what drew you to her in the first place, and think of the reasons that being with her made you so happy, I'm sure you can find the strength and motivation to see it through.
Guys and girls are wired a little differently...not so differently as some will have you believe, but it is true that women are more driven by their emotional sides than most men typically are. Chances are good if she ended the relationship with you that her emotional needs just weren't being met. You're going to have to do some changing in yourself and really let that be evident in you if you plan to try to get her back. She's not going to give the two of you another try if she doesn't feel that you'll be any better-equipped to provide her with the emotional support she needs.
The first thing you're going to need to do is get back into contact. Always remember that if it's been a little while since the breakup, she may be seeing other people. I know that has to hurt, but try not to barge in and ruin a relationship, it'll only make things worse. Use your best judgement when choosing a time to contact her.
When you do end up face-to-face with her, don't just try to convince her to take you back. Communicate, and don't forget that communication is a two-way street. You have to listen to her. Not only will she feel a bit more appreciated if you're truly attentive and obviously care about what she has to say, but it'll also make it easier for you to pick up on any signals or nonverbal cues she might give off.
And don't play around with her...make it clear through the use of subtle signals just what you hope for concerning the two of you. Don't "bare your soul" to her...these talks don't always work, and if you put too much down on the line you could end up being hurt pretty badly. But make sure that you avoid leaving yourself too vulnerable while still making it evident that you care about her, and always be attentive.
Another thing that can help you a lot is to make sure you're staying in shape. If you've previously had a couple pitfalls, now is a great time to work towards getting back into shape. There is very little in the way of motivation as powerful as trying to get back someone you love, and looking better than ever will certainly draw her eye.
Always remember as well that when you're making all these changes to yourself in the hopes of getting her back, you better be ok with the new person you become. If you just can't handle the compromises you've made, you're only raising the chances of further separation and heartbreak down the line.
Pagsure oi.... :D :D