Ask her for help or volunteer your assistance. The first strategy works well because girls are natural "fixers." They love solving problems and making others feel good about themselves. The second strategy is ideal because some girls like to feel you are trying to take care of them.
Borrow her pencil, calculator, book or lend her yours. Exchange phone numbers as you do so; after all, when you need your items back, you need to be able to contact her. Transform the contact phone call into a friendly conversation that leads to a date.
Suggest that you become group or study partners. Frequently teachers and professors order their students to pair into groups; don't be shy about asking her to team up with you. Suggest that you continue your study sessions over dinner or at a coffee bar.
Mention community events that relate to the class and invite her along. For example, you might say, "The local theater is doing a production of "Rent,""which just happens to be a play your drama professor mentions frequently in class.
Pass out flyers for a party or other social gathering to your classmates including your crush. This is a low-pressure way to invite someone to an out-of-class function, since it isn't a one-on-one date.
Sit next to the girl of your dreams. It may sound obvious, but one promising way of getting to talk to someone is to be near her physically. In college, if a girl sits by herself because none of her friends takes the class, she may appreciate your company.