How did the tradition of applauding begin?

Answer 1

From Wikipedia -

The custom of applauding may be as old and as widespread as humanity, and the variety of its forms is limited only by the capacity for devising means of making a noise. Within each culture, however, it is usually subject to conventions. The ancient Romans had a set ritual of applause for public performances, expressing degrees of approval: snapping the finger and thumb, clapping with the flat or hollow palm, waving the flap of the toga, for which last the emperor Aurelian substituted handkerchiefs (orarium) that he had distributed to the Roman people.[1] In Roman theatre, at the close of the play, the chief actor called out "Valete et plaudite!", and the audience, guided by an unofficial choregus, chanted their applause antiphonally. This was often organized and paid for.[2]

Sorry I can't be more specific. This is kind of like asking who the first guy was to see an egg coming out of a chicken's rear and thinking "Gee, that looks yummy!"

Answer 2

I'm sorry, I was just fooling around, trying to get information on this interesting question, and put in this link, made up by me.
I can't get to it... my PC has so many layers to it, sometimes things just don't work. Then again, though the link shows blue, it may not work either.
So please excuse me if I have wasted your time. You might go to a library and ask a research librarian to look into this for you. They are trained to do just this kind of thing, including the use of computers.
http://www.historyofapplauding.com
(.org worked, too... So I really don't know. Sorry!)