Starting conversation with girl?

There's this fantastic girl that sits next to me in diffy-Q. I was sitting there all class today and could not think of a smooth thing to say to her. The prof has assigned us partners to help each other with the math, so there's no reason to ask her math related question.

I thought about the weather, her clothes, her phone, etc but they all seem lame. She had an iphone so that is obviously not noteworthy. She was wearing jeans and a tshirt. Weather -blah.

Any ideas on something clever that would not be too obvious I'm hitting on her to start?

Just relax and be yourself; don't try to be cool or clever, but smile a lot. You could ask her what she listens to - tell her what you do and ask her opinion.

Here are my general suggestions.

To be liked, we need to be more interestED than interestING. Listening is good for making friends: ask people questions about themselves and their opinions and listen to them without interruption, except for little comments that demonstrate that you're Really listening. It shows you are taking them seriously, as in respect and acceptance. Don't sit there thinking about what you will say, because that shows more interest in yourself than them. Little pauses demonstrate that you are thinking about what they have said anyway. You can ask them how they felt about what they have just told you, or other specific questions to show you have been listening and taking them seriously.
Be open minded and try not to disagree with people. For example, if they like a band you hate, ask what it is they like about them, best track, etc. (avoid the word, "why" as it can sound challenging). You can always say you don't listen to them much but you will now or something. Asking for advice is also good. Genuinely, of course, & don't overdo it. Ditto information - we feel pleased to tell someone something interesting they did not know, such as what's on in town, latest sports score, etc., so by showing interest in their opinion, knowledge, etc. You'll get some good feelings from them. Smiling is a good sign of acceptance. A lot of eye contact can also be good.
Remember, if you want to have a friend, you have to BE a friend, and the best way to impress someone is to be impressed by them!
One thing you can do is always to ensure you have a straight back: sit, stand and walk tall (hips forward) and take reasonably long, confident strides when you walk: this has the "reverse psychology" effect of helping us to feel more confident. Once we have self respect and a sense of self worth, we tend to find that other people respect us more too.

Tell her you would like to take her out for a cup of coffee after class and see what she says. If she goes you will know she is interested, if not she probably doesn't have any interest in you.