I'll assume you've decided that things can work out between you and him, so now, the question is – what can you do so that he believes in your relationship too? This can be a huge motivator to any guy to get back together.
As mentioned above, you need to be better than what he remembers you to be. It's important that you don't see each other for some time, and then once you do – he is just blown away by how much prettier you've become.
Make sure you don't mess up, or he might never want to hear about you again, let alone get back together.
So, find out what messed up your relationship and work on it.
Were you too cranky, moody, jealous, demanding, insane, nagging-all-day, not giving him his space and freedom, disrespectful, got fat, made out with another guy, or you just sucked in bed? He needs to see that, after a month or so of breaking up, you are progressing; suddenly you became a different person. Once he sees how much different you became he'll wish you never broke up in the first place, he'll want to give the whole thing another chance too.
Then again, don't be clingy and don't call him every day after that – love all over again – instead, take your time. You had sex, but do you want to get back together or not?
Let him wonder and guess, let him compare you to other women he might have been with since you were apart.