Take the open seat besides her. Make sure you do not look like a creep inching towards her. If she sits down and you find a seat vacant besides her, just go there and take the seat with confidence. Your confidence will make her attracted towards you and she will probably ask you about your name.
Start with saying something nice to her. Make sure you do not appear like a typical person praising her eyes, hair and other parts of the body, because that is what others can say too. Nothing new to her! Yet, there is something that you still have the option to talk about. Yes, her smile. You can say that her smile is beautiful, which can make her smile again for you.
Now buy her a drink. Here, you might think that it is something really common in movies. Yes, it is. However, it is also the best way to buy some time to talk to her. The only requirement is that she accepts your offer, which will also make your confirm about her interest in you.
Tell her a joke, the one you can tell in a polite company. If you succeed in making her laugh or even smile, you once again will have a chance to compliment her smile.
Try to be artistic when saying good bye to her. You can take a napkin and draw her picture. However, do not do that until you know how to draw pictures. Otherwise, you can write her name using some beautiful personal font. Hopefully you have a good handwriting and calligraphy skills. Make sure you also write your name and phone number on it. She will definitely like to keep a napkin with her name or picture on it, rather than keeping a visiting card.