I need some tips on what to say to a girl...

Girls are people too. Just talk to her.

It's better to try and fail than to not try at all. Beyond that it's through doing this that attempts after it become easier. Is it hard to put yourself out there? Sure. Do you run the risk of being turned down? Yep. But in doing we become stronger and more experienced.

This world is full of people. Take a risk, you don't know her so do the simple and awkward thing. Introduce yourself, "Hi, I'm so and so. I have noticed you looking my way more than once would you care to talk?"

You already have the que of her meeting your eyes or looking at you more than once. So either you are visually appealing to her or you are a oddity to her. Either way put your best foot forward and make the attempt. The out come may just surprise you.

Actually, I'd be a little less direct than this (I think a lot of people don't want to be called out on staring, and this could put her on the defensive).

"Hi, I'm __. How are you finding the class? I think it's great/good/okay/hard (whatever, adjust accordingly)."

The class is your logical 'thing in common' and is therefore your ice breaker.

That is very true. Everyone reacts differently and approaches things in a manner that works for them. The point remains the same. Act or you will never know what the out come might be.

Cultures vary about staring. A lot of posters here, apparently from India, have talked about it over the years. In the US, far as I know, and I don't know everything, take it as weird, some kind of creepy come on.
Not creepy in some circumstances.

If you're both in the same computing class , why not ask her a question about a step in the computer homework or classwork. Be nice, not aggressive, not too shy, but get her to help you with your computer work.

Then ask her to have lunch with you at the school and then buy her a little piece of cake or a donut. You might find that she likes you and that you like her.

Who knows??