There are many ways relationships can get broken; most of the time the relationship is broken because of neglect. Your relationships are like gardens, if you don't take care of them and occasionally pluck out the toxic weeds it will die. This is where you need to begin healing a broken relationship.
Plucking out the toxic weeds that are chocking the life out of your relationship is what you should do first to start healing a broken relationship.
Those toxic weeds are the hurts, angers and disappointments the two of you have inflicted on one another over the time you have been together. Get rid of this and you will allow positive, life giving nutrients into your relationship.
To put it in more of a real world way; cut the crap. Sorry if that sounds crude, but it's a good place to start. Neither of you are perfect, more than likely both of you have done or said things that you know you shouldn't have done or said.
Step one then is to identify those things. Analyze your own behavior, and figure out why you lashed out and tried to hurt your partner (oh, and part of the cutting the crap is to acknowledge that on some level you did intend to hurt your partner. This is no time for sticking your head in the sand).
Now that you have a better handle on why you act the way you do (hint: in most cases it has something to do with some insecurity of yours) you can make efforts to not continually repeat the same mistakes.
Once you are courageous enough to face the fact that you are insecure about some aspect(s) of yourself you don't have to be uber sensitive and lash out whenever you are feeling insecure.
Instead, you can identify what is going on (your insecurity is rearing it's ugly little head) and respond to the situation more appropriately. Think how much nicer life would be if you could do that!
Think how much nicer life would be if both of you could learn to do that! When you get to that point, you can stop the toxic weeds from growing in the first place.
Next, you need to honestly and sincerely apologize to yourself and your partner. You need to let them know you are sorry for the pain you've caused but you also need to forgive yourself.
I hate to be the one to break it to you but you are not perfect! And that's ok. No one is. Be willing to give yourself permission to make mistakes, be willing to let yourself learn from those mistakes so you don't keep making them over and over again and be willing to forgive yourself those mistakes.
You may have heard the expression "physician heal thyself" well, that applies here too. If you want help healing a broken relationship start with yourself and go from there. If both of you learn and use this approach life can really be sweet!