That being said, don't get obsessed. Yeah, you asked her out, and maybe, if you don't have the best reputation, or she doesn't know you that well, (or you have a dead fetus attached to your left cheek) you might have gotten the "I'll think about it..". So, she says she'll think about it, and if she's worth your time, she really is thinking about it. She's talking to every girl that could possibly know you, and digging up dirt on you behind her back. She's showing pictures of you to her BFFs at slumber parties to see if they think you're worthy. Don't fret, if she's not a total bitch, she'll get back to you.
So, you're waiting for her to give you that response. Don't go to her every time you see her and give her the "So?" look. That will make her feel pressured, and the last thing you want is for her to feel forced into a date/relationship. Give her some space, back off as much as possible, while still ensuring her you're there.
Now, when she finally does get back to you, there's always a chance she'll say no, unless you're Mr.Perfect. So, the worst thing you could do when rejected, is get clingy and needy and desperate. She said no. Get over it! Once again, give her space. I've had my share of guys who won't get off my back, no matter how many times I try and give them the "hint". That just makes you even more unappealing, and it will make her feel worse for rejecting you.
Keep in mind the reason for rejection can vary. It could be for things she can't control, or her own reasons/decisions. So just because she rejected you, doesn't mean you will never ever get a girl.

Now, I'm sure if she means alot to you, you don't just want to give up on her. This is where you have to make her warm up to you, in a very subtle way. Give her space right after the initial rejection, but then start trying to get back in her books. Be cute/romantic, funny, helpful, and just nice to her, showing her that she might have made the wrong decision about you. This may sound like the "friend zone", but seriously, if you're a girl's best friend, you're almost her boyfriend, you just have to will her to take the next step.
So anyways, about impressing her... all you need to do is prove you are a good guy. Make her laugh, help her with her problems, whether they're school work or personal stuff, show her you're truly interested. Be chill, keep your head screwed on straight, and most of all, BE SUBTLE. If this girl has brains, she will take your subtle hints, while not feeling smothered or pressured.
Don't half ass it either. Keep yourself going by picturing yourself with her. Imagine the two of you having good times together (and try not to imagine all those good times being sexual). Imagine you being by her side, and aim for that. You gotta get the girl. You need to win her over.

I hope this can help some of you. Yes, I am a girl, no, I haven't had any decent relationships. But I have had a ton of guys fuck up the approach. Because that approach means everything.

Hey, so....um...I was wondering if, uh.....you wanted to, um...go see a movie with me?


No, but really, this is good advice, guys. Take it from a dude who's never been friendzoned.

I was once asked if I "would like to go out for a... hot beverage sometime, maybe on a Saturday or something". I know it was really mean for me to do so, but I laughed my ass off.

I mean seriously, how are you gonna go on a date with her, and possibly date her, if you can't even be comfortable asking her one question?

That one sounds good. I'm gonna try it later this week.

It's like one of those lines they put in romantic comedies to show the male lead 'doing it wrong'.
If it isn't already in one, I'm gonna go work on a script. That one is gold, specifically when said in a sultry tone.