How do I go about getting this girl to like me?

I like this very cute girl who works at the same place as I do, but I heard from someone that she might be having a boyfriend. I speak to her once in a while (each conversation lasting not more than 3-4 minutes) and how can I ask her if she has a boyfriend? people say that I am good looking (if not great) and there are a couple of girls interested in me, but I am interested and infatuated only by this one girl and I feel that I may never again love any other girl if I lose her. Please help how to go about this.