If it's a real clay shoot (not corporate entertainment) then be sure to ask people before you photograph them. A lot of shooters don't like to be photographed, for obvious reasons.
When it comes to the photography, watch the swing of the gun before getting into position to take shots, not all clubs are able to protect people from being at the wrong end of the barrel. If it's sunny, choose a stand where the shooter is backlit, this will add a lot of drama and backlight the smoke.