In order to reach this Book (and activate the mission), you have to head deeper into the White Ridge Barrow in the far north of Solstheim (on your way there you will have to fight our way through Moesring Pass. The dungeon isn't a nice place - by the very entrance you will come across corpses of Bandits. Deep in the cave you will be attacked by Albino Spiders and their more dangerous brothers - Flame Spiders. Defeating them shouldn't cause you too much trouble. Look out for the pulsating eggs - if you get too close to them, more enemies will hatch. Sneaking can stop that from happening, so thieves have an advantage here.
Reach the large room with three bridges and pull the chain by the middle one. That way you will lower the grate which will let you reach a big cave. Go below, deal with a couple more Spiders and Bandits and turn right. In the caves you will find lodes of precious stones and a passage to the further part - White Ridge Sanctum.
Form the cave that you just entered, you can exit using three paths - all filled with enemies. The corridor on the right leads to a treasure and a quite considerable lode of rubies - I'd definitely recommend checking it out. On the left you will find a mine (more rubies) and a cell with a strange machine which you can use to manufacture Spiders (nearby there's also a tunnel filled with spider-web and some enemies behind it). The Spider Recipe can be found lying on the desk beside the machine used to produce them.
The proper exit is however the middle one - also covered by spider-web. The Bandit protecting it has a key for the cell with the strange machine - just in case you have problems with breaking the lock.
In the cave to which you came now there is powerful Dragon Priest - Dukaan. He mainly uses frost spells: he can cast powerful spells and slow you down by freezing your character. IF you have a Resist Frost Potion, be sure to use it. Try not to step away from the enemy for one moment and deal as much damage as possible - note however that he's almost completely resistant to his own element.
After dealing with the threat, approach the wall with the Word of Power and learn the Cyclone Shout. Don't forget to collect the Mask that the enemy will drop - it gives you 50% frost resistance and increases damage you deal with this element. Afterwards take a look into the treasure chest and grab the Black Book in front of you.
Learn the Black Book's hidden knowledge
Strange rules are in force in the dimension inside the book. If you head out of the light and enter the shadow, the dark realm of Apocrypha will start sucking out your life. Therefore you will have to follow the fireflies and not get off the only possible path (alternatively you could use a torch or other source of light). At first it isn't hard - you just need to move forward, wait for your "guides" and avoid the deadly tentacles.
Things get harder later on - at some point you will come across three Seekers waiting in the darkness. If you can sneak well, you can pretty well ignore them - don't start an unnecessary fight. If not, kill them using a bow - if you run to them and start slashing with your sword, you will surely die (in fact the darkness will kill you faster than the enemies).
The further part of the realm consists of more corridors and... two Lurkers. The light is very dim here, so fighting them would almost surely end up with your death. It's best to just ignore them completely and quickly run through the rest of the path. Sneaking won't do the trick here - it's too slow and you will die in the darkness. A quick run seems to be the best possible solution.
After reaching the Black Book, you will be able to choose one of three options:
Seeker of Might
Combat skills are all 10% more effective
Seeker of Sorcery
All spells cost 10% less magicka, enchantments are 10% more powerful
Seeker of Shadows
Stealth skills are all 10% more effective
Before leaving the realm of Apocrypha, take another look inside the container beside the Book - you should find some useful items there.