If you are going to try to get your ex back, begging and pleading with them is not going to help you. These tactics are going to make it worse for you because you will be looking desperate for them, this is the last thing you need. Your best bet is to look like you are in control of yourself; even if inside you are screaming to them to come back.
So, avoid of the accusations of begging your ex and prove that you are doing just fine. What you can do and it probably sounds unusual, if your partner says they are leaving you agree with them that it's a good idea. It sounds kind of backwards but there is a reason for this.
When it comes time to getting them back it can make it easier because there was no fighting over the break up. The two of you separated peacefully and this will help limit any resentment or animosity towards each other. It can make it easier to talk to each other latter on.
After your partner has left you, break off any contact with them for a month. Do not call, email or text for any reason. Your ex will wonder what's going on with you and they may be more preoccupied thinking about what you are up to and can't forget about you because they have not heard from you.
Now that you can't contact them for a month it's time to get on with your life. Go out and have some fun with your friends or make new friends. Getting out will help you get your head on straight and get your confidence back. While you are having fun with your life your ex should also be getting past the break up and calm down.
After about a month give your ex a call and ask if they would meet with you at some neutral location. Make it sound like just a casual meeting just to say hi. When you do meet, explain that you have had time to think over your relationship and would like to apologize for anything you may have done to cause problems and maybe get a second chance.
Let them respond without you arguing back, be calm and do not bring up anything that may start a fight. Tell your ex to take some time and think it over, then say you must go and excuse yourself.