Yeah, I have this problem too. I get nervous, I think, "why would they want to hang out with me?" etc, but it is actually worth the risk of being rejected. If you never try, you'll never know.
Since you have friends think about what their interests are, see if they share any of the same interests, and do something, which relates to that. I personally love Disney movies and I know that one of my friends shares that interest. I tell her that I am interested in going to see whatever movie and I ask if she wants to come with me. Most of the time, the answer is yes.
The problem is that people get tired of having to ask if you want to do something/ talk it makes them feel unwanted so make sure that you have a "give and take" relationship with people. I appreciate that it is very difficult, but remember even "regular" people get nervous.
Good luck!