If you are very serious about getting your ex back then you need to be prepared to look within yourself for some answers. A lot of people get very caught up in the good times of a relationship right after a break up and do not take the time to consider some of the bad times that may have happened. I only bring this up because i would not want to see you in the same position a few months down the road.
Was your ex abusive verbally or physically? Did the relationship put you in harms way? If not then the chances are your relationship is part of the vast majority that can actually be saved. There a few situations that it is better off to just walk away. One other thing to consider is if your ex has some mental or emotional problems that would be helped if they were alone for a while. The majority of relationships can be saved but it is also important to recognize the very few that can and should not be.
Pestering and pushing your ex isn't a good idea. If you try to constantly get in touch with your ex; whether its by phone, email, text message, or stalking them you're going to do more harm than good. They will see this as a sign of desperation. This could actually push them further away than bring them closer to you.
Don't argue, beg, or plead with your ex about your past relationship. It's easy when you and your mind are all alone. Your mind manifests all sorts of wrongs that you may have done. Even when your ex broke up with you they may have gave you reasons why. Now, you're probably beating yourself up over them. You probably wish you had never done those things. The past should stay in the past.
The best thing to do in this situation is to step back and get your life together for you. This will help you in many ways. It will also send the message to your ex that they are really missing something by not being with you. it will also help you be a happier person and get more out of life.