How can I win my friend back?

their is a girl who hates me (im pretty sure)
I need to know how to win her back as a friend.
a lot of rumors were spread about us that were not true and I just need her to know that I want her back as a friend.

Rumors are horrible and ruin a lot of friendships. Well what I can say is take a look into the source of the rumors and figure those out. As for your friend, it depends on the girl. Sometimes you'll find one that understands social dynamics and will understand what just happened if they were purely rumors. If she's totally bought into what other people say or think and buy into that stuff then you can kiss your friendship goodbye. Like I said figure out the rumors and if she's stil angry then give it some time.

First you need to go to the source of the rumors and straighten them out...once you correct and prove to others they are false then you go to the girl and explain you took care of everything and the rumores have been proven false...and you apologize for the hurt it has caused and you hope that the two of you can be friends again....or if you can't speak to her face to face then e-mail her a letter...good luck...it will work but you will have to make the effort.