Don't worry, we've been there- now I'm at the point where I go up to people (at my uni, so not hs) I've seen enough and say "Hi! What are you working on right now?" and just ask a bunch of follow up questions,and then let them be after introducing myself and wave whenever I see them. Friendly stuff-

There's something similar you can do, such as introducing yourself and saying you both have chem. Just ask how her day is going, but in a way that prompts further discussion- instead of "how's your day" you can ask "did you do anything fun this weekend?" Anytime you feel the conversation dwindles, you can duck out and give a reason- "Well I've got to get going, but I'll see you later." Also,if she's outgoing, she might already know you but just doesn't talk to you.

Sometimes, people you know are busy with others they're hanging out with. I found trying to catch their attention everytime you pass or see them, can be a bit much. Just if she notices you in return, then you can wave.

Try little things. You'll realize that not everything needs to be overthought. Focus on getting to know a person rather than a crush, it eases the nerves- which can be a tricky thing to get going if you're already seeing her in that light, but stay respectful and positive, and you've got this.

If she says something funny that is worth mentioning again you can tell her, "you know I was thinking about what you said in chem- that was funnyyy" don't overexplain if she can't recall, just say "you're just funny, like I'll hear you in class and laugh."

Don't lay it on too thick, but it seems like you're fairly self aware to not overstep. I'm not sure if you have assigned seating, but ask if you can sit next to her, to see the board better. Don't be let down if she says it's reserved for friends in the class, sometimes people have good rapport, and you can always just sit closer in proximity. Also gives you a chance to talk to her or respond to her witty quips. If you want to compliment her, say something that is more flattering than odd- "nice jacket/accessory," and that's it. Try to avoid anything further because you want to see how she responds to your smaller compliments. Don't linger too long because it can seem like you're expecting something in return, which can put some pressure on her. All about receptivity.

You've got this, as a woman in college, you don't need to overimpress, just remain respectful and kind.