I'm not a step mom but I have a step dad and my husband is a step dad. As a teenager who suddenly got a "new parent" shoved into my life (I'm not a teeager anymore of course, but was when my mom re-married) there were some things that I hated more than anything:
1. The step trying to "play parent" with me, IE, trying to envoke their "authority" over me in "no uncertain terms".
2. The step trying to "be my buddy". Look pal, I don't know you, I don't love you, you belong to my mother (or father) not me so stop trying to suck up.
3. The step trying to take the place of the "missing parent". You are NOT my mom or dad, you are my mom's, or dad's husband/wife... let's leave it at that.

For a teenager and yeah, 13 qualifies, it can be nearly an impossible endevoure for a step to be invited into their "world". I use the word "invited" intentionally because basically, that's what has to happen. It is nearly impossible to be parent/friend at the same time but that is exactly what a step *needs* to be able to do.
To this day I can't stand my mother's husband and I DON"T consider him my "step dad" or even a part of my family... all because he tried to play hard ball with me and "straighten me out" according to *his* standards.... big mistake, especially with a teenager.

Don't smother her. Don't shy away from her either but... well, keep it "professional" for lack of a better word. She doesn't know you nearly as well as she knows her mom and dad and thus, she is not going to trust you. Also remember, respect is *earned* not *given*. That is a two way street. Don't expect her to respect you right off the top, you will have to earn her respect just as much as she will have to earn yours.... age and experience are moot in matters such as these.

Don't treat her like a kid. She's 13, chances are, she's going to want to be treated like an "adult"...do so. If she screws up, let her know it, but ALWAYS remember to let her know it when she's just being awesome! That is what will help build a foundatioin for a good relationship between the two of you.
If you have seen "step-monsters" first hand, then you already know what to *not* do.
I totally agree with Jo, let Dad do the enforcing of the house rules, it will work out a lot better and if she's going to get mad, she'll be mad at Dad rather than "the new chick".

Take several deep breaths, be who you are, don't hide your personality from her and just be willing to be honest with her but be gentle.