Its as easy as not caring at all about other peoples inner thoughts..
it is that simple ..in what they look like, in how they talk, how much they talk, how popular or unpopular they are, the list goes on ...
you have to zone out the people around you and approach every conversation by using deep thinking if you want proper discussions and whatever pops into your head on the spur as well, neither are necessarally more appropiate then the other though, so take your time if you like when someone asks you a question or even rattles off a joke or feel silly enough to say whatever comes first, dont expect that you have to respond within a milli second of them talking to you ...
most people will talk about themselves and their own interests because it resinates a confidence in them that can switch on banter that extends beyond hello, how are you, did you watch this show, sport ...
try and relax yourself and take your time ...
Also do you read alot? i dont know if it works for you but reading can enhance your memory and your vocabulary, your ability to think on the spot because paragraphs or lines of quotes and text can appear in your mind more often rather then going blank ..
show a fleeting interest in the news and learn as much as you can, it all helps with talking to people ...
i really dont know how else to say it, it is that simple ..
i'm not saying i'm an expert at all but the years when i didnt have any social anxiety that is how i felt, i just did not give a flying iguana what people thought of me and was able to zone in and out
but yeh you will need practice though it doesn't mean it'll take you a long time to get over this anxiety, it may take 3 or 4 goes and you'll improve and build on the momentum quickly ...
now regarding relaxing, if you feel like being around groups of people is really daunting try breathing in fast and out slowly and repeat that, i'd even recommend drinking and you won't become an alcoholic by doing this because everyone can control themselves, but people who become alco's are too weak to say "no" if its too much, just control your intake ...because it makes you tipsy and zones you out of your self conscious state which can have its benefits ...
alcohol can trigger your fun side to come out more often, if thats how you want to approach it, but using that method is instant the best way is too just teach yourself over time without that, i watch comedies, listen to audio books, that triggers me to be a sillybuns sometimes. ..