First of all, you need to establish exactly what the situation is.
Did you leave and wish you hadn't? Did you or your partner find someone else? Or was it all over a silly argument? The truth is that many couples will break up despite still having feelings for one another.
Indeed, it is very difficult to erase those romantic feeling which were there at the beginning of the relationship.
If you are really unsure of where the land lies, write a letter to your ex.
Whatever you do, do not sound too needy as this can be really offputting.
Instead, write a letter wishing them all the best and gently stating that you would like to get back together but make it clear that you will leave the ball in their court and make no further contact.
Knowing how to get someone back who broke up with you is not a question of hounding them-quite the opposite really as there is evidence to suggest that playing it cool and making your ex realise you have a life without them can make them feel sorry that they broke up with you in the first place.
If a meeting is suggested by your ex, make it short and sweet.
Suggest a coffee after work rather than dinner.
You don't need to explain.
Also, try to think about the character traits you had when you first met-were you more fun-loving? Did you both simply become bogged down with the stresses and strains of everyday life? If the coffee date goes well, how about suggesting a fun meeting next time? Maybe suggest an activity you both used to enjoy together such as bowling or skating.
Knowing how to get back with someone who broke up with you can be as simple as recreating some of the good times.