The bandits have stolen some artifacts from the mages guild's transport. Go to Camp Ales, one of their hideouts. You'll find two enemies in there. One of them (Bandit Carrier) will have the artifact - Dwarven Cog - with him. You'll also find an Undelivered Letter, listing the locations of all other parts of the mechanism.
There will be 4 new markers on your map, indicating the parts' whereabouts: Varus Camp, Bodean Camp, Dagny's Camp, and Brotch Camp. The thing is simple here - you have to visit them one by one and defeat the Bandit Carriers to grab the artifacts. You'll encounter one or two enemies on each spot.
Go to Arcane University and talk to Bothiel. When she leaves, wait 24 hours and you'll be able to enter the Orrery through a newly opened door in the Mages Guild Lobby (you don't have to be a member to access that area). Enter the place and start the machine by activating the Imperial Orrery Console. Touch it again to get a new skill, one that's depending on the current moon phase. You can come back here later, when the phase is different, to swap your ability with a different one. See below for a full list.
Each of the skills allows you to temporarily alter your attributes, increasing one of them by 20 points and simultaneously decreasing the other one by the same amount.