There are different reasons for people's being shy, and there are different types of shyness. How to reduce and or eliminate it, I think, just depends on too many things. Sometimes what seems like shyness is really just "reticence" associated with not being a bold person and/or someone who really has more confidence than is healthy. It doesn't help that there's so much bad information out there about shyness.
I think I may write a Hub about shyness, but it's a complicated subject for which the most "legitimate"/accurate information is really only found in "x percent" of the most "heavy-duty" research. The trouble is, however, that the harder-to-find "heavy-duty" research is kind of too-general and/or all-encompassing; and condensing that down in a way that covers the subject in general but also covers everything is kind of a challenge.
(I actually wrote a really long, "microscopic look", at the kind of "shyness" I have (even though I'm confident in a lot of ways), and I helped prevent the same degree of shyness in my daughter by knowing how back when she was at the age when preventing it was possible. The thing I have all written is too long and too "non-stellar" for it to be suitable on HubPages, though; so I'm back to square one as far as writing a Hub about shyness goes. There were reasons I couldn't prevent the same type of shyness in my sons, mostly because the type of activity required to do that wasn't available for little boys..
In any case, the particular type of shyness to which I'm referring (and it's more a matter of individual nature than an "anxiety") may/may not be something a person can eliminate. It may be something someone can live with, overcome, etc., depending on experiences and sometimes just growing up, maturing, etc.
Again, though, there are just far too many different types of shyness and causes for it for there to be a simple, one-size-fits-all answer to the question.