It's difficult and undesirable to persuade an ex-boyfriend to take you back if he's no longer interested. If you believe that your relationship still has potential, the best way to get your ex-boyfriend back is through sincerity, honesty and a commitment to fix the problems that led to your initial breakup.
If you and your boyfriend just broke up, give him some space before trying to get him back. In the first few days after a breakup, everyone probably is feeling tense and will be likely to respond emotionally, even angrily. Wait until you are able to think rationally about the situation before approaching your ex about getting back together.
If possible, meet with your boyfriend face-to-face to talk about fixing your relationship. Pick a neutral place to get together, such as a coffee shop, restaurant or bookstore where you can talk uninterrupted.
When you broach this issue with your ex, don't pressure him or make promises that you can't keep just to get him back. Be honest and tell him that you would like to get back together, point out the good things about your relationship and begin to discuss what factors led to your breaking up in the first place. Even though you probably won't be able to work through everything in one day, addressing your problems directly is a good step to showing him that you're committed to creating a healthy relationship and aren't jumping into things without thinking them through.
Be sincere, but not overbearing. Although it's important to show your ex that you still care about him, it's important to avoid pressuring him by sending repeated emails, phone calls, or text messages if he doesn't respond favorably to your advances. If your ex-boyfriend is giving you signs that he wants to take things slowly, respect his wishes and focus on being his friend before approaching the subject of getting back into a relationship.
It may also be tempting to try to get your ex back by making him jealous, but this technique rarely works. While there's nothing wrong with casual dating and flirting after your break up, there's no need to go out of your way to let your ex know about it. This may send him mixed signals and leave him unsure about whether you're still interested in him.