I am a quiet person. That is not to say that I never speak. On the contrary, when I know someone well, I can carry on enlightening serious conversations with friends. These very same people cannot, however, believe that I am quiet, because I can talk to them. I suppose I could be called a shy extrovert, because I enjoy a good conversation maybe more than anything else. I find nothing more rewarding than to just sit and talk with a friend.
The reason that I do not like to talk with strangers or when I am first talking to someone, is that I want to avoid embarrassment by saying something offensive to that person. That problem is easily avoidable after I know more about a person and their beliefs.
I know I am a quiet introverted person, and I do not need someone else to tell me that. How awkward is it if someone comes up to you and says "You don't talk much." I mean, what is an appropriate answer which avoids embarrassment? I welcome someone who wants to come up and talk to me. How else am I going to get to know you? Just please don't center the conversation around my introversion. We can save that for later.
To talk to a quiet person like myself, you should start the conversation. Keep on talking for a minute, and let me get comfortable with you. After a minute or two, I will probably open up to you. Don't go expecting a radical change. It is a gradual process. Don't rush it. I can almost guarantee that if you give a quiet person time they will open up to you. In a lot of cases we are like an oyster, if you open us up, you are likely to find a pearl inside.
It should be noted that the notable exception to this advice are those people suffering from a serious antisocial personality disorder. They can be dangerous and are best left alone.