Can you show that you've learned from all of the mistakes in the past? Can you improve on things that didn't work before? How often were you out with your girlfriends instead of being with him? You should know that is a recipe for failure and an eventual breakup.
What you should do is let him know of all the good things you had together in your relationship. You need to be that girl you were when you first met. I'm sure you were an attractive girl to him with a lot to offer.
Did you stop being and stop doing the things that made him want you?
Since you've broken up with your boyfriend, a good approach is to show your ex boyfriend that you still care.
Show him you still support him, and will do things to support him. You may only be friends now, but with this attitude and support for him, things can surely change.
Perhaps you did things and behaved in a way that his friends weren't to fond of you. You need to fix this as his friends may have a lot of influence on who he should date.
Another tool you should use is to have you and your boyfriend reminisce about all of the good times both of you shared. The more positive things you can put into his mind, the better the chances are for him to reconsider getting back with you.
Remember to always look the best you can. You can never tell when you might accidentally bump into him. Guys are so much more visual than girls are, and if he sees how great you look, that could trigger a great desire to get back together with you.
Don't be a downer! You have to be a positive happy person. Guys don't want to be with a depressed, whining girl. Show him that you are the type of girl who is happy and upbeat, especially around everyone you know.
In the end it's especially important that you don't look like you're obviously trying to get him back. Lay back and be cool. Let him come to you. He will when he sees that you have the qualities that guys like.