Send her a letter. Girls also love letters, because they take a lot of time and you have to express your feelings. Start off by saying something like: "I know this letter doesn't fix what's broken between us, and maybe it never will. But I want you to know that I care deeply about you, and I always will. That part has never changed. The part that's changed is that I realize how stupid I was to let you go."
It may be hard to go through your daily routine without her at the moment, but you're going to have to learn how to, since the only way you win her back right now is by being patient and giving both parties some space to recollect their emotions and feelings for one another. The other guy sounds like a rebound right now, and you'll have to let their relationship fall apart on their own before you make a move.
You'll have to try and figure out what it was that made him break up so suddenly with you before you can determine the steps to take. For the time being, focus on self-recovery and pick yourself up from the breakup and perhaps even come to terms with it. If not, you won't be able to take the proper steps in trying to win him back. You can apply no contact for now, and when you've recovered, to attempt in re-connecting with him. Hopefully by that stage he would have unblocked you and be more receptive towards you.