how can i introduce myself to her?

[no name]

have a dating question.i am 16 and a male and go to a small school.there is this one girl that i like.she is a czechoslovakian exchange student who is staying with a girl in the grade above mine.i don't know her and she doesn't know me and neither does the girl she is staying with.she has been is school since january and i think is going home by the beginning of april or possibly sooner.she is quiet and always stays with the girl she is staying with all the time and really have any other friends.i have nt classes with her but see her in the hall and sometimes have lunch in the same period as her, and every few days her and her friend come to my study hall class to talk the study hall teacher.she does speak english but i dint know how well.i am kind of shy and not the most popular but am not in that bad of status and want to go out with her or at least be friends with her and stay in contact as she lives in the czech republic.i am not sure what to do as i only have about month left and really like her.can you offer some help on what is should do and how i could ask her out?(i know nothing is capitalized as i typed fast)
i would like to introduce my self to her but i am not sure how and dont want to want to just go up to her out of the blue ?