Personally how I got over my social anxiety and awkwardness was by powering through. Realizing the things I thought I handled horrible didn't even blimp on peoples radar during or social interaction. Just being me was more then enough, and to stop trying to be the person people liked (not in a popular way, but in a don't want to make people uncomfortable long story). I would suggest you find one person and go out of your way every day to make small talk even if it is just seeing how there day is going. Once you get comfortable with that you be surprise how easy it is to approach others, and expand your social circle.

Also a side note even the most social person can be really antisocial. At one contract I had we had one guy lets call Joe that was the social butterfly would setup after work gatherings for the team and everyone seem to like. One day at lunch one of our co-workers was going through some bad stuff with his family, and Joe was pressing a joke on him that was getting him so upset that I had to hold back the co-worker from beating Joe. After lunch when I got Joe by himself I try to explain the situation, and why the joke wasn't consider funny and such in case it was just going over his head and he didn't realize what he was doing. Come to find out Joe understood, and did it on purposes. Joe actually disliked everyone on the team, and his way of blowing off steam was basically picking really random fights. You wouldn't think it from looking on the outside, but after learning that I start realizing all sorts of things.

Be polite, be considerate, don't take anything personal, don't over think it, and be yourself. I know easier said then done, but you got to go at it if you want change.