You walk around in a non pvp world for around 10-20 minutes
The Left Skull Half is dropped by Ankous on the fourth level of the Stronghold of Security.
Your skull will go away after spending enough time away from a PVP area.
If you have been skulled, all you can do is avoid re obtaining one in combat, and in about 21 minutes it will go.
The skull sceptre is a non-rechargable item. Much like the games necklace or ring of duelling, once all charges have been depleted the staff crumbles to dust and you need to get a new one.
It's off the peninsula of Daemonheim.