You've got to prepare yourself for some major humbling. Seriously, get ready to say, "I suck," and "You were right and I was wrong." I would write down beforehand what I wanted to say and in what order, and even practice it. Confrontation makes me nervous, and I've had to do this with a roommate before... Even in parts where I thought this other girl was in the wrong, I humbled myself to see it from her perspective-- since I knew we were stuck living together for awhile. A good apology shows you understand the point of view of the other person and does not give excuses to justify the bad behavior. It is also made in person, and while you can meet at a public place, it should only be between the apologizer and the apologizee. (If you bring a friend for "moral support," the person is going to feel "ganged up on" and get defensive.) Make sure you don't get defensive, either; stay calm. Also, tell the person why (s)he is important to you-- why you want to keem him/her in your life. You can do it! A good apology really is a good experience for you and will help you be really great at being in all kinds of relationships in the future. Good luck!

Simple. You say I'm sorry. If person refuses to accept it then I'd say forget it. You can only do what you can do and unless you went out of your way to destroy someone purposefully or betray someone, you need say no more beyond "I'm sorry".