I've had a few automatics, and currently drive a diesel with a traditional (though very modern) 6 speed automatic box.
Much prefer auto to manual for the kind of driving I do. Most modern autos don't have the kickdown button on the floor, they just sense the position of the pedal and change gear accordingly when you want to overtake.
For country roads, I tend to switch across to manual control, and as someone has said above, modern automatics change down a gear or two when going downhill to enable engine braking. I wouldn't have a manual now (though the wife has one so I'm not totally out of practice).
American automatics, on the other hand, are absolutely rubbish in my limited experience of rental cars. No torque from the engine and utterly gutless.
EDIT: to the OP, unless the hill is very steep, they just hold themselves on the hill or creep forward slightly if you don't have the brake on. Right foot does everything, and it takes minutes to get used to.