I feel for you brusus, that is frighteningly similar to how one of my first relationships ended. Six or eight months into it she met somebody else, I tried my hardest to win her back (I even repaired her microwave! Then she moved out of her apartment a few days later and left the microwave :shrug: ) but she stayed with the other guy.
I spent that summer with my friends, did lots of crazy stuff, met somebody else and spent a year and a half with her before we broke up.
Point is that even though breaking up with someone is always a shitty thing to do, to be fair, she wasn't happy. She shouldn't have started with somebody else before telling you, of course, but relationships come and go, some for the better and some for the worst.
I was lucky that I met somebody so soon afterwards. Sometimes that happens and sometimes it doesn't, but you can help everything along by accepting it and moving on, hanging out with friends, being productive, achieving other goals and cutting off all contact with your ex-girlfriend. I wouldn't recommend calling her and being friends, that will just be a constant reminder to you that you can't have her. If you want to be friends then do it later on, after you've moved on and there are no lingering feelings.
Just give it time, and don't give it any thought, and you'll be fine
