When you break up with somebody (or when he breaks up with you), your relationship is officially over, but you may still have feelings for him. The sting from the end of a relationship, however, can alienate an ex and, in some cases, he might not want to talk to you at all. There's no surefire way to make him resume the relationship, but by keeping in mind some tips --- and avoiding some key pitfalls --- you can increase the chances.
Avoid seeming over-apologetic, or, if he was the one in the wrong, like a victim, but don't speak to him as if nothing happened at all and you can start completely anew. Initiate conversation for a reason other than the fact that you want him back --- wishing him a Merry Christmas, for example, or asking how his final exams went. Showing that you still care about him, regardless of what happened between the two of you, will speak volumes about your intent.
Call rather than sending a text or email --- it's more personal --- but avoid showing up at his home or workplace uninvited, as this might be interpreted as harassment. If he doesn't answer the phone, leave a message explaining your reason for the call. Even if you're sure he's ignoring you, don't mention this in the message.
Give him time and space if he asks for it. Although you may have already decided you want to take him back and have fully made peace with the reasons for which the two of you originally broke up, he may need to sort through things on his own. Keep in mind that although your relationship was collective, your current state --- as ex's --- is individual on both sides.
Enter back into the relationship slowly once he comes around. Even if the two of you were nearing engagement or marriage before you broke the relationship off, taking your time in getting re-acquainted with one another can help you spot potential problem areas before they become serious. It will also allow you to make sure you have made the right decision in getting back together.
Talk to him about the reasons he stopped speaking to you, but don't use his answers as a means of attacking him. By listening to him and expressing empathy for his reasoning --- regardless of whether or not you agree with it --- you will show him that you respect him and he, in turn, will respect you more.