I have a Sportline with the flappy paddles. You have one on each side of the wheel to manually shift up and down gears. That can be done on all DSGs via the drive selector anyway. To drop out of manual just hold in the paddle and after a few seconds the DSG will go back into auto.
I have to be honest I really don't use them that often and find them a bit of a gimmick, I have used them in snow when I don't want the DSG to change gear and I want to use engine breaking to maintain speed downhill, just allows you to keep both hands on the wheel whilst you shift gears.
I would probably argue that generally the DSG in auto is far more efficient and faster accelerating than most people trying to change gears using the manual mode although more fun paddling, it's only useful if you want to hold the gears longer but that said Sport mode does that for you. You can change the box into sport mode and back into standard by pulling back the drive selector, also worth noting this only changed the gearbox mode (gearbox mode and be vehicle mode are not the same thing), the cars setting in sport mode changes allot of other things other than the gearbox response including steering , ride, auto start and lighting responses amongst many others.
I personally find ECO mode a waste of time as it doesn't seem to give better economy.