Help me approach her?

Hmm...not saying this to be mean, just stating the fact. You appear to lack any level of confidence and the associated courage that comes with that confidence. So, really? Anything we tell you will be useless because you won't have the confidence to carry it out. If you did have any courage at all, I would suggest that you simply walk up to this group of friends, say hello and apologize offhandedly for interrupting and to this girl, "Hey, could I talk with you a minute?" She WILL say yes. When you have her aside from the 'pack', simply tell her that you'd been thinking about her and was wondering if the two of you could...you pick...get together or something.

It really is that simple and straight forward. The more you think about it...over think about it...the harder it will be.

Don't give her anything. That's weird and creepy.

Walk up to her from the front, smile and say, "You know, I've seen you around and I still don't know your name. What do you like to be called?"

She'll tell you her name. Say, 'That's cool, nice to meet you <name>." And then walk away.

Say hi and call her by name in the halls the next month or so and talk to her again later.

Don't try to strike up a conversation in the middle of everything. Be quick. Less than 30 seconds. Say hello, introduce yourself, keep things moving.

You can go up to her with a simple and friendly smile and give her a rose for friendship