Walk up to a girl and make up an excuse why you need to talk to her. For example, you can ask her what time is it and/or what is for lunch today (and what she recommends). This is traditionally called "breaking the ice," and is a way to make the conversation branch out into other discussions. When talking, look her in the eyes and smile at her. If she makes eye contact and smiles back, then you can take the conversation further. If she does not, she is not interested.
Hold out your hand and shake her hand. This is a sign that you are courteous and think of her as a person and not an object. Exchange names and let her know you are glad to meet her. To make the conversation go further, compliment her on her clothing, hair and so on. Allow her to thank you and be playful with her. When she asks you a question, do not give her a direct answer and keep her guessing.
Ask her about herself to let her know you are interested in her. Ask the girl questions about herself and look her in the eye, letting her know you are interested in what she has to say. Talk about yourself a little bit if you want, but do not make the conversation completely about you; this will make a girl think you are cocky which is a turnoff for many girls. Once you feel you have a strong connection with one another, feel free to ask her on a casual date where the two of you can talk in private. If she is interested in you, she will say yes and the two of you can talk for hours.