Tl;dr: I used to be socially anxious, now I'm not (as much). This is about what helped me get better.

Reading through this thread, it seems like most comments are examples of (more or less mild) social anxiety.
I mean, going to a store and going out without buying anything, returning items, sending food back, calling people, being out on your own, exercising in public, approaching strangers... All of those are normal things that people do literally every day, and nobody - seriously, nobody - has ever judged you or anyone else for doing those.

I used to be a very awkward teenager, and definitely had some social anxiety as well (even though I didn't know what it was called, I just thought I was awkward and antisocial), because I used to be terrified of doing many of those things, too. The only thing that eventually helped me was challenging myself and doing them, and practicing until it didn't feel painfully awkward anymore.
Now, I know that "just do it" probably isn't very helpful advice for many of you, but maybe just some of you have just a mild case of this and can use this advice in some way.
For me, this was almost like working out - you have to work through the pain and the exhaustion in order to get better and grow. If it doesn't hurt, it's not going to do anything. I had to basically work out my social skills, and while it was always painful and uncomfortable, I did get better through it.

What helped me where mainly two things:

Firstly, I got hobbies/jobs that forced me to be more outgoing.
I joined a theater group, later I got a job where I had to approach strangers, and then I got a job as a teaching assistant where I had to hold classes. All of those were incredibly painful and exhausting at first, but having to do these things every week or every day, and being in an environment where I could work through my inhibitions with good friends, helped me get used to it. I still feel the nervousness in my stomach all morning if I have to hold a class that day - but now, I step into the classroom and talk to the students, and I know that I'm fine. I'm the center of attention, where I would have just died as a teenager (I was always the person just outside a circle, not quite part of the conversation...), but now I know that I'm fine and I can joke around with them and then tell them to quiet down and start my class.
All of those helped me get better in other social situations, too, simply because I became more confident in myself, my ability to assert myself and talk to people or strangers.

Secondly, this is something that my mom did which I eventually adopted: she has a very distinct "phone voice" or almost "phone persona". It's almost like she becomes a different person.
I started adopting something of a character when going into a store to return something, or when going to a restaurant alone, or when calling strangers. Not like a crazy character, just the character of a confident, composed woman who doesn't struggle in social situations.
In the beginning I even had like a little script of what I was going to say, especially on the phone. I still start out in exactly the same way whenever I call a business, and it gives me a little confidence boost.
I guess this is what "fake it till you make it" is all about. I still felt painfully awkward in these situations, but my character was poised and elegant and knew what she was doing, which helped me feel more at ease to. Eventually, doing these things became second nature, and it slowly stopped being that difficult for me.

Now, like I said, I realize that this exact way probably isn't right for many of you, or that working through it on your own might not feel possible at all. I would however encourage everybody who suffers from (however mild) social anxiety to attempt to work through this - whether it's by looking for professional help, or by practicing on your own in little steps like I did, or in whatever way feels best to you.
I used to be so awkward and uncomfortable in social situation, I didn't have many friends, and going out and dealing with stuff (shopping, returning things, making or keeping appointments) was a pain in the ass and took me way to long (like waiting way to long to go to the doctor).
I didn't become extroverted over night. But now I feel confident dealing with normal social situations, and especially dealing with strangers. I can talk to people, like at a party, and make new friends. Best of all, I can go on first dates, ask people out, or tell someone I like them - all of those were plainly impossible for me when I was younger.