Dot...Let me tell you about my situation and what God has done, because it is directly related to the question of how to get close to people.
I am a very introverted person, much like it sounds you are, and talking to people is not high on my list of comfortable things to do. Last year when I got saved my mom pushed me to go to a meeting of a Christian group on the campus of my school. My first reaction was "there's not a chance in the world I would consider that, I only barely know one of the kids that attends". But she kept telling me I should go, so I finally said I would go once and see what it was like. I did go and it was awkward...very awkward. Honestly the first time I went I thought they were a little weird, not really the type I would want to be around. I stuck it out for a couple weeks because the teaching was good. Now I go every week that I can, and I'm getting to know the kids more and more. I just got back from a five day trip with some of the kids...something I don't really like to do. The point being, you have to step OUT of your comfort box if your going to get anywhere. If I would have never stepped out of my comfort box and went the first time, I wouldn't have gained the friendships and fellowship that I have now. Just step out of your box and you will be amazed at what God will do.