How will a girlfriend come back to you after a breakup?

write a song or do something realy romantic for them :

Doing something romantic is a good idea but you need to be careful of how you do it. You ex girlfriend will not be interested if you appear to be crawling back to her.
What you need to do is concentrate on yourself, making sure you project a confident attitude. Be well groomed, dress well and show you can be independent.
Your self esteem is more than likely low after the breakup and you need to work on building it up. Go out with friends and family and have fun. If she sees you out and about she will start to wonder what she is missing.
Keep in contact with her but don't overdo it by harassing her with constant SMSs and phone calls. When you do contact her be understanding, listen to what she has to say (you might find out why you broke up). Be sympathetic, helpful and above all don not put pressure on her to do anything.