“Black Book The Sallow Regent” is the Side quest in Skyrim - Dragonborn
This is a somewhat straight forward adventure, but you will want to bring in a torch, the spell Candlelight or another portable source of illumination to make things easier. The darkness in this area will be able to damage you. Have light will hold off most of the damage.
Start by heading out of the light to the South.
This will lead to a safe zone with a pool that has an eye staring out at you. There is a pod you can open for some loot to the West of the Eye.
To move forward, turn to the South. There is a light there that can work as you guide forward. Head to the light.
Once there, turn to the West and run through the corridor. This will lead to another illuminated portion of the area where you can recover some.
This will bring you into a large room. This will have a few Seekers. Just how many depends on the player's level. It can be between 2-4.
The exit out of the area is to the South. You can skip navigating the whole of the room using the moving light sources just above your head by running there. This will also put you against a few Seekers that you should fight. Fully exploring the room will yield some books and more Soul Gems.
Turn to the South and head through the dark archway just past the light.
Head on up the slope at a run and into the light on the walkway beyond it.
The first bridge here will raise and retract at intervals. You will need to wait for it rise and then run across it to the light on the far side. There will likely be a Lurker. Be ready for them. There is likely a Soul Gem on the table on the left-hand side of the landing on the table.
Go on up the stairs to the South. Follow the Walkway as it go back to the Northwest. Run to the light at the next landing.
on this landing, turn to the West and wait for the bridge to raise. Cross it once it does.
Follow the walkway as it winds around the next book pillar and goes upwards to the South.
At the top, head either into the light on the left or right. There is a Lurker in this area that will be hunting you. Be on guard for it. Either lure it into the light or go into combat with a torch if it is not in an illuminated.
Having dealt with the Lurker, you will want to head to the South and go up the stairs there. Try to travel with the light source as it does.
At the top you will find the Black Book itself and be able to activate one of its three powers.