Dear Sarah,
Whatever you did made your friend very angry, so give her a little time to cool off. Then approach her again and explain that you really want to stay friends. Sometimes, just saying "Sorry" is not enough. Maybe you need to tell her a bit more. Another idea is for you to write to her—by email or with a cute card—explaining how you feel.

Dear Sarah,
Give your friend some time. She can't stay mad at you forever, so just let her cool down for a few days. Then you should try to apologize again. If you constantly apologize, it might just get her more upset. Hope all goes well.