I've got a problem...

Yesterday I got in a small, let's say, discussion with one of my friends, and I think I upset her, but she won't talk to me reasonably about it, and I'm not sure how to handle it. I keep thinking about it, and how I should have handled it differently, and now I don't know if I should let it blow over, and hopefully it will be fine (you know, ignore it and it will go away..) or if I should try talking to her again. Thing is.....I don't know how to do it, if that's what I decide to do. I'm not good at stuff like this. I can normally get out of it by kidding around, but that didn't work. The hardest thing for me is that she is acting like everything is fine, but she said some things that tell me there are other issues besides our discussion yesterday, and I think in reality she has the wrong impression regarding my part in these "other issues". I guess my question is - How do you say I'm sorry when you've already said it? - Do you say it again, and again - or do you say it the one time and don't worry about it anymore? Should I even try to fix it? I don't know what to do. She's my friend, and is important to me, I hope she knows it.