I did what Skeezyks suggested I volunteered and made some of the best friends ever, I agree shared interests and passions are a good place to start. Volunteering, hobby groups, sports groups, lots of people on here post positively about online local meet up groups (although I haven't tried this myself).
When getting out and about my advice to you would be to take things slowly, not to fret if things don't go as you hoped, it's like mud on the wall - sooner or later you'll find some great people you can click with.
You sound like an open sort of person and probably don't need this advice but I'll write this anyway - keep your mind open, curious, interested, listen to people and find out about them. As a quieter kind of person you'll probably find you're good at that, but also when you feel ready share a little of yourself too (that was something that didn't come so easily to me, but once I cracked it friendships developed).
Good luck