Love is an unexplainable emotion and it causes people to do crazy things. However, what do you do when the recipient of your love is taken from you? One who is not under the love's spell would move on, let it go, and realize that if she has left you for someone then it is their loss. But not you! You are crazy about her and you, until you're dying breath wins over your body, will not stop loving her and will do anything to win her back.
The first thing you have to realize is that there is something the new person has that you don't. You need to examine this and the new person she is with. If that person seems to be more ambitious than you, then simply you change yourself to appear more productive. Take up hobbies, read some books, try new things, and maybe apply to more prestigious jobs and if you're still in school be more involved in your studies as well as the community. If he is better looking, as much as you don't want to, admire him. By doing that, you can learn from him. Sure a lot about looks are genes, but dressing, demeanor, and hygiene is not. Dress better than him, act better than him, and look cleaner than him. If by now she still has not chosen you over him, then there is one thing missing: fun. When you were together what did you consider as dates? Were you content with movies, food, and long walks at the park? Do something exciting show her that with you she would not be settling, she is one lucky person to find a catch such as you. Be more outdoorsy. Show that you are interested into just the norm. This fits in with you and your new hobbies. Go scuba diving, go snowboarding, go to art shows, and go dancing. Do anything, but make sure whatever you do doesn't look like it is apparently to impress her. You want to win her back and that also means improving yourself. Do things that you are genuinely interested in. Do not under any circumstance start drinking, partying, and posting pictures on face book of you with a bunch of girls to get her jealous. It might make her jealous, it might not. But it will not make her think of you any better than her person now and shows immaturity.
If all else fails there is sabotage. However, that is morally wrong and in the long term will not benefit you, her, or your relationship.