This unmarked mission is one of the biggest challenges offered by Skyrim: Dragonborn. Its course is rather untypical - firstly you have to go to the Glacial Cave in the north and obtain Karstaag's skull (you will have to defeat three Rieklings on your way). It's the easiest part of the mission.
There are two paths leading to the throne room in which Karstaag rests. The first one - Castle Karstaag Ruins - requires you to break the master-level lock which might be very challenging. If you lack patience or skills with the picklock, choose the second option - Castle Karstaag Caverns.
If you chose the path through the cave, you will have to fight your way through a large city inhabited by Rieklings. It shouldn't cause you too much trouble - the enemies are numerous, though the construction of the area is very easy and you won't get lost (while you're at it, you can also complete Recover the Bonemold Formula for Glover Mallory). Just head onwards all the time and kill the enemies on your way until you reach the throne room - the room which you would have reached at once if you had broken the lock.
Stand in front of the throne on which the skeleton of Karstaag rests and place the skull found in the Glacial Cave on it. Afterwards immediately move away to a safe distance - the ghost of the monster will resurrect, causing an enormous explosion which can kill you. You will have to fight for your life - Karstaag will immediately attack you.
The beast from the north is one of the toughest and most difficult enemies in the game. The beast is completely resistant to ice, poison and disease and also absorbs most of shock damage. Increased vulnerability to fire isn't a big consolation - Karstaag is constantly surrounded by a cloak of ice which deals rather high damage (therefore fighting him will be made very difficult) and has powerful attacks. The cave is small so you won't be able to run away from the enemy, so you will have to fight him in an ordinary way. If you have some potions protecting from ice and physical damage, be sure to use them as otherwise you rather don't have a chance. It's also a good idea to bring companions - you however have to keep in mind that they will likely die after receiving a single hit. The best way of defeating the enemy is reaching 100 level in Sneaking - that way you will receive a perk which allows you much easier assassinations. Shouts and special skills provided by the Black Books will also come in handy.
In return for defeating the beast, you will receive an unique power - summon Karstaag. The mighty beast will fight for you - which pretty much means winning every fight. There is however one limitation - you can only use it three times before it becomes unavailable.