Where to go from here?

So in one of my University tutorias, this HB9 was sitting beside my usual spot. A little later our instructor asked us to break off into groups with the people you were sitting beside. So we started talking and were hitting it off pretty well. She even introduced herself to me, which is a huge ioi. After the group discussion our instructor continued and we didn't really have another opportunity to talk again. I couldn't think of anything to say to her after dismissal, and she went to go talk to her friend, so I didn't want to follow her for obvious reasons.

My question is, what should I do the next time I see her, whether it is in one of the dining halls, hang out spots or next week during class? I feel like this is a golden opportunity that has fallen into my lap and I want to execute it as best as possible.

Thanks.

Just open up and talk. You have a common theme and that is class.... A majority of people's problems out in the world is they feel like they are intruding on someone else by talking to them. Out at a bar, you find something to talk to a girl about. Then you develop conversation over topics and common themes.... In your case, you already have that common theme aspect.
Who cares what you say. Just say it with confidence and just talk. If you truly are at a loss, ask how her day is. I wouldn't go with that, I'd try to be more creative, but who cares... Compliment her on her shoes or shirt or whatever (not her looks though).

Poke fun at her too. Be friendly, but flirtatious.

Years back when I was in college... I was sitting in my class and some random girl who I never spoke to passed me a note making fun of what the professor was wearing. It struck up an entire conversation and we ended up hitting it off. Anytime I saw, I'd give her my cute "i'm sexy but mysterious" smile and she would smile back and talk with me.

You already have that foot in the door, so go ahead and take advantage.... Best thing to do, ask for her opinion on something because we all know girls love giving opinions after opinions on anything and everything.

Mr8Hyde6 has the right idea. Just go up and talk to her. Use your first encounter as fuel for the next. You've already gotten the hardest part of meeting someone, the introduction, out of the way.

Do all of the above. When you feel like its time, try to go for her number (make her want to give it to you and look up some number lines for getting it smoothy) also since this is a class, you may feel like your putting her on a pedestal and she's the prize. Remember, your the prize, and she is working to get you.

Dude, she was probably just being friendly because you were in a study group together. That said, next time you see her, be honest, tell her you enjoyed talking with her and would like to take her out.