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The easiest way to begin a conversation with someone you want to talk to is to ask a favor. You don't know this person yet, so you don't know what you have in common. Asking a favor is a neutral way to enter into conversation without boring them with something they don't care about. Make sure it's a small favor that won't put her out. For example, ask to borrow a pen or read their class notes to see something you missed. If you don't have your textbook, ask to look on with her. That way, you can sit closer to her, too! Since you don't know her very well yet, you might not know what she likes. The only thing you know for sure that you have in common is the class you're in with her. Even if you understood the class lecture perfectly, ask her to clarify something the teacher said. As opposed to asking a favor, which can result in a very quick interaction, asking someone to explain something to you will probably result in a longer conversation. Keep the conversation going by asking follow-up questions. If she didn't understand either, show solidarity! Let her know that you're in it together, and that you have something in common. Girls love guys with a sense of humor, so try to make her laugh. Make eye contact with her when somebody says something silly, or roll your eyes when the teacher assigns homework. Make sure you're not disrupting class, though, or drawing the teacher's attention. Getting in trouble will not impress her! You're looking for anything that begins a speaking relationship with her, so make her feel like you want to know what she has to say. Ask her something related to class, like what she thinks is going to be on the next test, or how many hours she's planning on putting into preparation for a presentation. Don't talk over her when she gives her opinion. Let her talk for as long as she wants, and show interest in what she has to say. Giving compliments is a lot trickier than it sounds. You may think "who doesn't like getting a compliment?" but you should always be respectful of girls when complimenting them. Always complimenting girls on how pretty they are sends the message that you only like them for their looks, and most girls don't like to be made to feel that way. Compliment her on something she actually had to work for, rather than something she was born with. This might be related to her appearance or not. Compliment her on her hairstyle on a particular day instead of her eyes. Compliment her on an outfit she put together. Tell her you liked her answer to a question in class. Congratulate her for doing well on a test if you see she got a good grade. Don't bother her with questions or favors if you see that she's concentrating on something or she's late and has to run to her next class. If you have a class with her, you're going to see her every day, so wait for a time when she seems relaxed and in a good mood to break the ice with her.
Ask a small favor. Ask a question about something the teacher said. Make her laugh. Ask for her opinion on something related to class. Give her a compliment. Choose the right time for your icebreaker.