Once the skull has been obtained, take it to Castle Karstaag Ruins. The ruins can be entered two ways. The first is through the front door, but this requires picking a master-level lock. The other method is traversing through the Castle Karstaag Caverns, which houses an entire tribe of Rieklings.
Once the castle ruins have been reached, defeat the Rieklings that have taken up residence and place the skull upon the large throne. Once the skull is in place, the ruins will rumble and begin to shake. A spectral Karstaag will appear from the throne and immediately attack. Once he has been defeated he will vanish, leaving only his ghostly remains.
As a reward for defeating Karstaag, the power of Summon Karstaag will be granted which allows the Dragonborn to summon the beast to aid in battle. This power is unique in that it can only be used three times, after which it is no longer available.