Oh, if only there was a simple way to do this! Perhaps the technology is just around the corner that will let us practice with a virtual boyfriend until we get it right - they're trying to come up with better "Artificial Intelligence" all the time. In the meantime, the rules for every boyfriend are different. But how to reunite with your ex boyfriend will always have some basic elements in common.
One of the most obvious is seeing if he's attached to someone else. If he is and they're serious, it might be too late. This is why you shouldn't dither around if you think that you might have a future with a man, let him know right away, because men tend to be impatient and they want to move on quickly.
Now try seeing if he'll at least talk to you. If you've just broken up, give it a few days at least to cool down - important for you as well as him. Now just message him 'what's up?' and 'just seeing how you're doing and how you're feeling about us.' This is a nice way to phrase it - you're not coming on like a desperate, clingy crazy, and you're not making demands or giving him ultimatums.
Now here is the part where there are individual approaches to reunite with your ex boyfriend. He might be willing to stay 'just friends' with you for a while - fine then, that's an in! He might be open to getting together with you once in a while - the 'friends with benefits' angle. Maybe that's a good strategy, and maybe it's not. You don't want to end up being bed buddies on the side while he dates another woman. Still, if you're serious about reuniting, it's better than nothing. See if you can work in a conversation about how things were between you and whether he'd like to try it with you again.
If you do get to this point, don't let your insecurities discourage you. Remember, if he let you get this close, he's at least interested. Just don't make him feel threatened or like you're trying to trap him. Keep things light and casual. If a few months go by this way, point out that you're spending some time together and getting along so far, and that maybe it's time you two got back together for 'keeps.' Happy hunting!