- What a foul and unnatural weapon you wield, I've never seen it's like." - City Guard, when weilding the Skull of Corruption
Skull of Corruption is a dream-dependent weapon of different usage than its predecessor during the Oblivion Crisis. It can be obtained in the quest Waking Nightmare, which begins in Dawnstar. At the end of quest one will be asked to kill priest Erandur or destroy the Skull of Corruption. Choosing not to kill Erandur does not make obtaining the Oblivion Walker achievement impossible, as there are sixteen possible artifacts to collect. Although there are only fifteen, unless you break/abuse the questIll Met By Moonlight.
In order to collect dreams to power the staff simply cast it on a sleeping person. This is not counted as an aggressive action so they will not attack you. A good place to collect dreams is The College of Winterhold, as it is easy to get full access and there are lots of people in a small space sleeping during the night.
Note that you still have to keep the staff charged with Soul Gems as well.
If you have the Skull of Corruption equipped, guards will comment about it, calling it "such a horror."