Recently...they've kind of just adopted me. I'm incredibly shy, but I had been going to a little local coffee shop (just to get out of the house) and always tried to be kind and engage with the people working there when they would talk with me. I had a few really emotional weeks, and one of the owners picked up on it. She handed me a note with her number, and let me know I could always talk with her. She ended up inviting me to a little Halloween pumpkin painting night with some of her friends, and I connected with them super well! Now they invite me out to little activities, food, movie nights, etc.
That's kind of how I've meant most of the friends I've had- be kind, be interested, and be present! People get more comfortable the more they see you around, so even if you're a little shy or awkward, someone might extend a hand and bring you into their circle.