I guess just be as honest as you can. Say you looked it up online and think you have it, then share the information with them. As far as I can tell, my family just think I've suffered depression and 'some' anxiety in the past. They don't seem to realize it's a huge problem for me today. I haven't told them because I know they'll just think I'm making excuses for not getting on with my life (i.e, that I'm hiding behind my SA). It's getting really frustrating because they keep pushing me to apply for jobs that involve a lot of communication with others and/or dealing with customers a lot. As it is I'm working for the dole right now in a shop (mostly out the back, thank God) where they occasionally put me behind the counter. It's so terrifying. I feel accomplished about doing it but at the same time, I couldn't imagine doing that by myself in a real shop.
There is alot of information about SA on the internet that you can show them so they can understand what SA is. Hell there's even a wikipedia entry: http://en.wikipedia.org/wiki/Social_anxiety_disorder
Just be as strong as you can, do your best to set up a comfortable environment and tell them you have SA. At the same time, show them the information from the internet.
If you still can't tell them, then another idea is maybe the next time you go see your GP doctor for a checkup, Tell him and then you can have him tell your parents or even refer you to a psychologist.
I've actually never been able to come out and tell my parents that I have SA. In fact, I keep it hidden from them the most.
But.. If only I could do things differently, I would have come out and told them when I first realized what was going on, rather than spending 15 years suffering in secret. But of course the SA kept me from doing that. So I really hope you are able to tell them and get help.
Well the way I told my parents....
I had a massive breakdown one morning before school (body shaking, crying, incoherence) and begged for help....worked for me! But I wouldn't suggest it, haha. I would give them info from a book. Some parents really don't think anything on the Internet is trustworthy.