1st Tip on How to Get Your Ex Girlfriend Back: Apologize Sincerely. We're assuming it's your fault. Think about what you did. Put yourself in your girlfriend's shoes. How would you feel? Think about what you would want to hear if she had done or said the same thing to you? In this way, you'll start to realize that what you did was wrong from HER point of view. When you apologize, do it sincerely addressing what you did wrong in a frank, forthright manner.
Don't make excuses! Don't qualify your apology and don't blame her for your words or actions. If she still has feelings for you, a sincere apology is one of the best ways to prove to her that you are worthy of a second chance.
2nd Tip on How to Get Your Ex Girlfriend Back: Act like you just started dating. Girls want to feel special. She obviously feels hurt - that's why she borke up, right? She is hurt and/or annoyed with your behavior so guess what you have to do to get her back - change your behavior. Start listening. Do nice things for her. Romantic things like you used to do before you started seriously dating. Be creative. Flowers and chocolate are good but they may not be enough. Think about how you can really make her feel special...then do it.