Social anxiety tends to be caused by excessive monitoring of your internal emotional state and the reactions of others. That is, you analyse yourself and the situation too much. This might sound weird, but if you can find a way to think less during conversations and be a bit more spontaneous, you'll find it goes better.

If you were seeing a psychologist about this they would put you through cognitive behavioural therapy, but I take it that's not an option so all you can do is treat it like training. Practice social interaction until it becomes second nature. Accept that you will make mistakes (everyone does) and they might be embarrassing, but it's not the end of the world if you do. Every experience of social interaction makes you cooler, more easy-going and nicer to be around, so long as you don't go out of your way to be a bastard. Good luck and godspeed, anon.