If you catch a girl starting at you often in an admiring way and not in a weird way, she might be interested in you. And if you look back at her and she shy away pretending that she wasn't looking at you, then she might be interested in you. Some girls simply admires a person for their looks and personality but without any intentions of getting to know you. Who knows probably that girl had been hurt in the past and she just wasn't ready to go into another relationship with another man.
You can start by making an excuse to talk to her if you get a chance. Usually within the first conversation you would come to know if she is interested in you. If you detect a hint of boredom in her way of talking with you, then you know that she is not for you. At least she can't be your partner in life if she is behaving like this within the first few conversation. If she wants to know more about you and seems to be interested in everything that you are saying and she in return is willing to share everything about her honestly with you about her past, then there is a good chance of getting along for the both of you. Most important thing in a couple should be the free flow of communication and information between them. Lack of communication and mistrust will spell trouble for the couple. Remember, choosing a partner is for life and not for a few months or few years. If you two can't have a good conversation every time you two meet up, then how will the both of you go through life together as a team without proper communication between the two of you.