New to America USA, how do you socialize and meet new people?

I recently moved to the USA, from the middle east. My English is pretty good, and I don't have a lot of trouble communicating with people at work or in stores. I also don't know anyone here at all, outside of work. All my family is still back in Gaza, and I've been here over a year now, and still feel cut off from American people and culture.

How do you make friends and socialize here? How do I learn more about America and Americans culture? I know a bit about history, but not much about anything else.
I don't drink or go to bars, for religious reasons. I have joined a couple of clubs based on hobbies, but still feel disconnected. I'm not sure how you socialize or meet new people here, in my family everyone came around your house all the times of the day, and here it seems like neighbors just stick to themselves. I don't want to bug people or anoy them if that is not the customs here.

Also, what are your favorite parts of American culture and history? So far I have enjoyed Nascar and monster trucks very much, and studying mathematics.