Skyrim:The Cure for Madness

Quick Walkthrough
#Speak to Astrid.
#Find Cicero's journal and take it to Astrid.
#Behold Astrid's horse, Shadowmere.
#Travel to the abandoned Brotherhood sanctuary outside Dawnstar.
#Choose to either kill or spare Cicero.
#Return to Astrid.

Detailed Walkthrough
Cicero
thumb|Cicero feigning injury deep inside the Dawnstar Sanctuary
When you return from completing the Breaching Security contract, Gabriella will inform you that there was an incident with Cicero and directs you to discuss it with Astrid.
Astrid reveals that Cicero attempted to murder her and the other members of the Dark Brotherhood, grievously wounding Veezara in the process. Arnbjorn pursued Cicero as he fled from the sanctuary. She asks you to search Cicero's room for clues as to his whereabouts. Inside the room you find five journals, with the final journal indicating that Cicero might be headed for the long-abandoned sanctuary outside Dawnstar.
Astrid will grant you use of her horse, Shadowmere. Immediately outside the sanctuary he will rise from the black, bubbling liquid. Mount him if you wish, and head to Dawnstar's abandoned Brotherhood sanctuary.

Dawnstar Sanctuary
You will find an injured Arnbjorn outside the sanctuary. He reveals that he and Cicero seriously wounded each other before Cicero escaped into the safety of the sanctuary and instructs you to "just follow the blood".
A pass phrase is needed to enter the sanctuary; it can be found in the final volume of Cicero's journal ("Innocence, my brother").
Once inside, Cicero will begin to speak to you, taunting, as you search for him. 
At this point, summon Lucien Lachance for a bit more on the story. He strongly suggests that the Dread Father would not want you to kill Cicero.
While the sanctuary is abandoned, it is not unoccupied. It is inhabited by ghosts of the previous Dark Brotherhood residents, who will attack on sight. The elusive Udefrykte also resides in one of the sanctuary's caves; it may be advisable to simply sneak by the troll when discovered.
As you make your way along, the second room is a circular chamber with another room below and a bridge. The spike trap can be avoided by avoiding the bridge and crawling along the left-hand wall; there is enough of a ledge to allow this. 
Across the bridge at the foot of the stairs, you will find two skill books: Fire and Darkness and The Marksmanship Lesson. 
Keeper of The Old Ways
At the end, you will find Cicero curled up in a fetal position, apparently injured. Cicero cautions you that the Night Mother will not be happy if you kill him. At this point it is your choice whether to kill him or not. If you attack him he leaps to his feet, obviously unhurt, and gleefully screams "Haha! Behold the final trick of the Fool of Hearts! You think me near death? Haha! Think again."
If you decide not to kill him, he returns to serve and tend to the Night Mother after you complete Hail Sithis!. He will also be a follower. 
Whatever your decision, the quest is now complete. Speak to Astrid to begin your next mission.

Notes
While killing the ghosts under the bridge, there is a ghost that can be pickpocketed for a bow and a large amount of arrows.
It is possible to pick up the weapons used by the ghosts, but they are difficult to find and disappear very quickly. The weapons are dropped in the same manner as any other NPC's weapon when killed. Since you only have a couple of seconds, it may be easier to tap the action button repeatedly and follow the weapon as it falls out of the ghost's hand.
While the quest is active, Lucien Lachance will continue his dialogue on "the jester" and the Dread Father, even if you are nowhere near the Dawnstar Sanctuary.

Bugs
 
 
 
 
This also appears to work with a crossbow .
 
 
 
Not sure if this has been fixed, however my follower worked properly both inside the sanctuary and left with me.
 
To fix this, load to a previous save, or during Death Incarnate, coax enemies near the pool to lure Shadowmere out via his aggressiveness. You can also try fast traveling to all the stables until you see Shadowmere for a split second afterwards, and then fast travel back to the sanctuary's pool to see if he has been untrapped.
 Open the console and enter   followed by   and then   and Shadowmere should appear in the pool as normal
 
Reloading an earlier save may fix this.
 
If Gabriella does not meet you at the entrance walk out and walk back into the Sanctuary.
 
 

Quest Stages