The most important thing that you should do first is that you should apologise for your behaviour with her. Do not bother about how your relationship ended up. Just call her and say sorry and also say that you still love her passionately.
Try to meet her in a gathering of friends because a gathering makes the things light and you can spend more time. A gathering of friend helps in avoiding uneasiness that otherwise can prevail when you meet your ex-girlfriend alone.
You should try to keep things light by talking different things with your ex-girlfriend. Try to include jokes in your conversation that will help in making her mood better.
Try to have fun in a gathering and try your best to involve your ex-girlfriend which will show your care for her.
When you feel that she is feeling better, then try to spend time with her alone and show your love for her.
Try to resolve things by saying sorry for everything that caused break up. But try to talk in a light manner and avoid making the situation serious.
Convince her with your behaviour that you still love her with the depth of your heart. It will help you in getting her back in your life.