You seem too nice to actually take any solid action, so you better build your move slow and over time.

Study well.. be a good boy in the classs and build an image. Be good and nice.. At the same time let her know that you are interested in her by smiles and casual talks in the class when it is natural to do so.

Try to sit next to her 3-4 classes later and strike up a conversation... Sit there again for the next classes and when you are more confident and comfortable, invite her out and take on by your own...