I'm anxious in social situations—and accordingly, very awkward. I'm making this list first for myself, and I hope it can help others to think positively rather than let their anxiety debilitate them. (For clinical anxiety, I realize that more than just positive thinking is needed.)
1) It's very common, even normal.
A lot of people, not just you, have trouble in social situations. Even those who seem completely confident might be doubting themselves or feeling anxious. A lot of times when you think others are judging you, they actually aren't thinking about you at all.
2) Fake it 'til you make it.
Surprisingly true, this saying can help you to put on a confident face and demeanor until it comes naturally. Stand up straight, make eye contact, and smile. Be willing to talk about yourself and ask questions about others. If I'm honest, I'm still in the "fake it" phase, but I've heard from reliable people that it works!
3) It's not always your fault.
In some cases, people you find awkward to talk to are that way for a reason. They hold eye contact too long or leave awkward silence, maybe because they are anxious or socially inept. Don't assume that it's always your fault. Chances are, you are doing nothing wrong. Just be extra kind and patient.
4) Don't punish yourself.
When you make a comment not well received by your audience, don't punish yourself. Don't replay the moment over and over in your mind so you can kick yourself and make vows never to do/say that again. Shake it off, forget about it, and keep engaging.
5) Be you.
Try not to overanalyze everything that you want to say. You should be known for your true self, not for some version that hesitates to speak out of fear of being awkward. Find people who value what you have to say. And when you do run into difficult situations, remember your group and how they love to hear your thoughts.
Please don't let fear lie to you about your worth or steal your presentation of your real, awesome self. If you're an introvert, accept your social preferences as who you are but also push yourself to new heights. Good luck!