How can i earn her forgiveness?

freshmen in college, fell in love with this gorgeous girl, but of course she has baggage. I really love this girl, but shes still in love with her ex whos at home and she still tells she loves him and makes him feel like hes the only one in her life...just like me. But i started hanging out with some of her friends and theyre alot of fun, but theres this one that i really like being with. I've been kind of dating the original girl but without the title, just doting upon her and being there for her, but sometimes i would hang out with her friend and i would have so much fun. I would forget why i thought i liked the other one more. I'm not much for commitment so that might have just been me wanting what i couldnt have. I had sex with the orighinal girl i loved, but me and her friend kept getting closer. We didnt really do anything but i spent the night in her bed a couple times, fooled around and dry humped but nothing too big. I decided to "break up" with the girl id been kind of with, and i told the friend i had sex with her. So now girl i love is being pushed away so forget about her, the problem is her friend. I really like her, not love like, like we were in the process of starting a relationship but couldnt because i was in a a messed up little scandal thing. But i hurt her...everytime i would go back to the girl i loved my stomach would churn, bc i knew how much it hurt her. After i told her i had sex with the other girl shes really upset. I did it bc i didnt want her to find out from someone else, like she wasnt important enough to tell. But i hurt her too bad, and she says she doesnt want to talk for awhile. I dont know what to do to make her see that I'm sorry, that im ready, that im done saying one thing and doing another. How can i apologize for being so foolish? How can i gain her forgiveness?