Should I try to talk to a girl a 2nd time

Say, "Hi, Julie (or whatever her name is), did you get that most recent assignment?"
Or "Have you been able to follow the professor for the last chapter?"
Or "Is this a great class, or what?"
Or something like that

In short, talk to her like you would to any other classmate. You really don't know each other well at all, but you have a big thing in common already, which is a HUGE ice breaker.

Have a few of these conversations, sprinkled over the course of maybe another month. And start saying hi to her when you see her on campus, or just wave.

Then ask, "I'm going to the ___ (whatever the local non-bar hangout is where they serve beverages) to get a ____ (coffee, soda, smoothies - this has to be something without alcohol). Wanna come along?"

And see what happens. If it goes well, then say, "I had a really great time. Can we go out on a real date, say, Saturday night?"

If it goes poorly, then no one's done anything embarrassing. And if she says no to going, it might be because she legitimately wants to study, or maybe she'll tell you she's got a boyfriend (or a girlfriend), or she's busy but maybe another time would be better.

You don't have to follow this script to the letter, of course. But something like this. Even if all you do is say hi a few times and it doesn't turn into anything, you'll have done something terrific, which is to reach out to another person. Even if it doesn't work out, as you can see, these things can make you nervous. Get some practice under your belt and you won't be quite so nervous next time.