What should I do if I like a girl and I am afraid to start a conservation with her? How do I know that she is interested in talking to me?

Find a common point of interest. It doesn't have to be anything big. Maybe you're both in the bookstore and you notice that she's in the fiction section, you can say something short about how you like fiction books. You can find out if she is interested in talking to you by her tone of voice, body language, level of eye contact, facial expressions, and overall the level of attention she is giving to you. A simple thing you can also try is, after making an initial comment, say, "Hi my name is _____." If she follows up and tells you her name, she's probably interested in continuing the conversation.