Online:The Mad God's Bargain

Quick Walkthrough
# Talk to Valaste at the Mages Guild in Rawl'kha (Reaper's March), Evermore (Bangkorai), or Riften (The Rift).
# Place the books in the pillars of light.
# Talk to Shalidor.
# Enter Eyevea.
# Meet Shalidor at the Guildhall.
# Talk to Sheogorath.
# Close the portals.
# Place the crystals near the Guildhall.
# Confront Sheogorath.

Detailed Walkthrough
To Eyevea
This quest will begin once you've reached Mages Guild Rank 5 after completing Chateau of the Ravenous Rodent. Passing any Guildhall will cause a projection of Arch-Mage Shalidor to appear before you and direct you to the guildhall in Rawl'kha (Reaper's March), Evermore (Bangkorai) or Riften (the Rift). When you arrive, speak with Valaste to learn that she has successfully translated the final tome. Help Shalidor by placing the four books at the ritual site to open a portal to Eyevea.

Once you arrive, Shalidor will inform you that the island has indeed been returned to Tamriel, but Sheogorath neglected to remove its Daedric guardians. Follow Shaildor to the island's guildhall, which has been magically sealed, and speak to Sheogorath. He will reveal that the Daedra are intended as a final trial to overcome to fully release Eyevea from his influence. Shalidor will instruct you and Valaste to travel around the island and close portals to the Shivering Isles while he works on unsealing the guildhall.

Close Shut the Marble Jaws
There are three portals dotted around the island, and many Daedric guardians blocking the way. Each portal has a crystal, and you need to collect the three crystals, either by fighting, or by sneaking and taking it. Valaste will occasionally make inane comments, seemingly sinking ever further into delirium, but she will continue to help you fight. Once the portals are closed, you will need to return to Shalidor and place the three crystals in three braziers outside the guildhall.

Once inside, Sheogorath will confront you. As a final test, he will force you to single-handedly battle Haskill wielding the Wabbajack. Once you are victorious, the Mad God will concede defeat and relinquish his hold on Eyevea for good. At this point, however, he will draw attention to Valaste's worrying state, and propose a sinister bargain.

The Folium Discognitum
Sheogorath will reveal that he has slowly warped Valaste's mind through the four tomes she had translated, and will demonstrate that she is now in a state of complete madness. In reference to Shalidor's original loss of Eyevea, he will offer you a deal: he will either cure Valaste of her insanity, or give you the Folium Discognitum and take her back to the Shivering Isles with him. In practical terms, the Folium gives you two otherwise unobtainable skill points. Curing her earns you her thanks, and she grants you a purple Frost Staff from the Shalidor's Curse set; other items to make up the set can be crafted in Eyevea.

After making your choice, Sheogorath will depart and Eyevea will populate with Mages Guild members. Your decision does not influence your reward from the next quest, The Arch-Mage's Boon.

Notes
To other players, Valaste will appear as a Guild Battlemage while following you during this quest.
Sheogorath mentions that the Folium Discognitum is worth half a dozen skyshards (i.e. 2 skill points).
 

Quest Stages