I've been working with the very same problem. I sometimes get intensely lonely and just want someone to talk to in person who isn't also a trained psychologist. :/ It's partly a matter of numbers: the more people one's exposed to, the increased possibility of (potentially!) making a friend, but I'd be lying if I said I'd gotten anywhere yet myself. Hopefully you will have better luck, but from what I've discovered (and really known all along) is that you can be in a room full of people, but without that damned instinct to take the initiative and make the first move in a conversation, it looks futile.
I signed up for yoga classes 7 months ago with this quest forefront in my mind. I really did think I would make friends this time around: yoga interests me and it does help me, but I unfortunately don't socialise with the other women there at all. They all talk to each other, but not me. The times I've tried to say something nice to one of the others, but I never say a word and they probably think I'm extremely rude. The instructor is nice, but she is very busy managing the classes, so we exchange pleasantries but little else. In any case, I think joining extracurricular classes, groups, and anything that catches your interest is still a way forward. If nothing else, it all adds towards making us more interesting human beings.
_________________
On hiatus thanks to someone in real life breaching my privacy here, without my permission! May be back one day. +tips hat+