I thought it was if you are riding in a snaffle (w/ a horse under five, then they are graduated to a shank or curb I believe) or a bosal you ride two handed. Otherwise, it's one handed. Please someone correct me if I'm wrong!
Your both right. In most shows, a horse that is under 5 is permitted to be shown in a snaffle or rawhide bosal. Both of those are to be ridden with two hands. Anything over 5 must be shown in a curb bit with one hand. As for where your hand should be, that really varies by discipline.
This seems to pretty much be the norm in the WP ring, though the thumb should always point up. Puppy paws are puppy paws in english or western, one or two handed.