Let's address some of the things that should be your primary focus even before worrying about how to get back an ex.
Even though that question may be foremost in your mind, you will have to address the causes of the break up and how to correct them if possible.
If you can resolve those differences initially, you will eliminate most of the stress and tension that accompanied the split in the first place.
If your boyfriend dumped you, there is a possibility, if not a probability, that it was due to one of two reasons.
The first is that the relationship was not holding up because you were not involved enough.
The second is that you were too involved and were causing the relationship to become claustrophobic.
Either one is not good, so you should evaluate the break up to see if one of these was the cause.
Whatever the outcome of your evaluation, if it ends up that you were basically the cause, it can be a difficult thing to accept.
It can be harsh to look at the break up this way, but if it was because of something you did or did not do, then your first step is to change whatever it was that drove him away.
In any case, you will have to take a hard look at which of the things that led to the break up were your fault and which were not your fault.
You can rule out the ones that were not in your control and focus on what you can change.
It may be an oversimplification, but if the split was due primarily to something you can and will change, then there is a very good chance you understand how to get back an ex and will be able to re-establish the relationship.