Here's my thoughts, as someone who's naturally shy, socially awkward (or maybe just plain weird), and loaded with anxiety issues.
Start small. Don't try to make friends at first, just practice interacting with people. Ask totally random people questions you can Google. Is the 6 train running on time today? Is this the way to Market Street? Do you know a good coffee shop around here? Ask people in social situations personal questions that aren't too personal. So what do you do? How long have you worked here / gone to school here / known Jim / lived here? A lot of people don't realize I have crippling social anxiety, simply because I have mastered the art of small talk.
Practice being uncomfortable. I'm assuming you've got a healthy dose of social anxiety, like most introverts. Wear opinionated tee-shirts that make you feel judged. Try going to random meetup groups, not to meet people but just to practice feeling awkward, silly, and watched. Try the juggling and unicycle unicycle meetups, and spend an hour falling off a loaner unicycle in front of everybody. Practice making smalltalk. How long have you been doing this? How long does it take to learn how? How many balls can you juggle? What's the most impressive feat you've seen performed on a unicycle?
Establish a routine. Proximity is important; you can't make friends if you're never in the same place twice. Go sit in a coffee shop and read the paper every morning, go for a run at the same time every week or day. Find a couple of meetup groups and attend them regularly.
Online friends can be real friends. Even if you never meet them, if they care about you and vice versa, an online friend counts. Making your online friends in-person friends is also pretty awesome. I made several good friends online, and now about half of us live in the same city (most of us live in two cities). We hang out from time to time, play board games, see movies. Most of us have worked together at one point or another.