What can I do to not make my step sister hate me?

Have you tried talking to her? Often times all you really need to do when presented with a problem like this, is talk. just ask her if you can talk to her, and then explain to her that you harbor no ill will against her, and you'd like it if the two of you could work on whatever problem you have. alternatively, she may just dislike you or distrust you for no real reason, and it may be something that cannot be helped. all in all, try to find a common interest, or goal, and build on that.