Starting this quest doesn't require you to complete the Cleansing the Stones quest. If you are doing that quest, however, then save the Sun Stone for last because it is likely going to be right on the way to Noleth's home. From the Skaal village, start travelling to the SE. When you get to Tel Mithryn, you'll find Noleth's apprentice practicing outside. You don't have to talk to him but feel free to talk to him and Noleth's Steward if you'd like. When you are done, head into Noleth's house.
As soon as you step inside, you'll find that there's a blue stream of energy traveling up at the spot where you are standing. Simply activate the stream to float upwards. At the top, you'll be in the house proper and find Noleth nearby. Talk to him and he'll tell you more about the Black Books. He'll tell you that the book he has isn't useful to you but he knows where there is one that will likely help. Follow him out of his house (be sure to "float down" rather than fall to your death).
You'll need to travel to a Dwemer ruin just NE of the Sun Stone. When you get there, you'll have to fight off a medium size group of Reavers. There could be as many as 12-15 of them around this area with a variety of attack styles from magic, to ranged, to melee. Work your way slowly through the outdoor area and use the buildings themselves for cover when you need to. You can also always jump into the water and swim down a little bit to protect yourself but you have to be careful when resurfacing.
Get to the other side of the ruin and you'll meet up with Noleth outside. To open most of the doors or activate the levers in this ruin, you'll have to use a special cube like the one he uses to open the doors here. When they are open, head inside.
Nchardak
You'll immediately enter the room with the Black Book but it's under lockdown right now and you need to activate the steam engines in the ruins to open it up. You'll have to be patient with Noleth. There are a few spots where you'll have to wait for him to stop talking before you can proceed. Eventually, he'll open a nearby door that leads to an elevator. Take the elevator down to the lower levels.
When you get there, you can walk ahead to a spot with a few machines and a couple of pedestals. Unfortunately, you're going to have to wait for Noleth to finish his little stroll before you can continue on. He'll eventually put the cube onto one of the pedestals and the water in the room will lower. When that has happened, you can grab the cube and follow Noleth. He will head back to the long terminals and then announce that he's found other cubes in the building. Follow him to the next door and open it with the cube.
You'll notice that this pedestal is red instead of blue. Red indicates that it's a toggle so once you put the cube in, it will unlock the door and you can remove the cube. It will stay unlocked until you place the cube in there again to lock it. Blue pedestals require the cube to stay in place for the pedestal to function. Go through the door.
Nchardak Workshop
Inside the workshop, walk ahead and turn left to find a pedestal at an intersection. Grab the pedestal and go down the ramp just beyond it. As you go down, a couple of Dwemer spiders will come up at you. Take these out from a distance if you can because they explode when they die. Continue past them and you'll come to a large room where you stand on a bridge. Cross the bridge to the far side and place one of the cubes into one of the blue pedestals. Keep the other in hand.
Below, you'll see that the water has lowered. There will be a red pedestal in the middle of the floor which is still partially submerged. Not far from that will be a bridge on the next level up. Off to one side of this bridge will be a red pedestal as well. Activating this red pedestal will raise the bridge. After it is raised, take that same cube and place it in the red pedestal in the middle of the floor. This will create a staircase leading from the bottom, up through where the bridge was and leading to another doorway.
Go through the doorway at the top and this will bring you to a T-shaped room. If you go right, you'll come to a room with a chest but if you go left, you'll find a room with a single blue pedestal and another cube. Grab the cube and head back into the large room. Take the cube from the pedestal above. This will raise the water level higher than it was when you entered the room.
On the fourth side of this long room will be a doorway with no door. If you go inside, you should now be able to swim across the broken walkway to the far side. Continue along the hallway and it will lead you out of the water. You'll enter a new large room with a really tall ceiling. Follow the only path available and watch on the right side for a little nook with another blue pedestal. Grab the cube and continue along the path. The water level will begin to rise again and a Dwemer Centurion will spawn behind you. Kill the Centurion and watch for the Ballistas at the top of the stairs.
This will bring you up to the highest point in the room. In the middle will be a red switch. Activate it to lower a bridge. The bridge will lead you back to the beginning of the workshop. From here, take the door back to the main room of Nchardak.
Back in the Great Chamber, place two of the cubes in the pedestals at the top of the room. This will lower the water level enough that you can access a couple of doors below. Follow Neloth to the doorway on the right side and use a cube to open it.
Nchardak Aqueduct
The Aqueduct is a rather large room with a cross shape lower level submerged in water. Walk towards the center of the room and then turn around to see two ramps that lead back up over the doorway that you came through originally. When you get up to the platform, you'll see three red pedestals. You need to use these to lower all of the bridges at once so that you can cross to the door on the right side. To do this, activate the left most pedestal and then the right most pedestal.
This should lower all of the bridges. Hop down to the lower level and walk across the left bridge. Take the stairs up to cross the high bridge and then come back down stairs to cross another lower bridge. When you do this, be careful of the Dwarven Spheres Spiders that appear. When you get to the far side, climb the stairs and at the top will be a blue pedestal. Place a cube and the water level will lower in the middle.
Jump down to the lowest level and open the far door with the red pedestal. Go up the ramp and follow the hallway beyond but when you see a room, stop because there's a trap. Flanking the doorway will be two blade doors that can close and hit you coupled with spinning blades in the middle of the room. Wait for the opportune time to cross (or Whirlwind Sprint across) into the room beyond.
Inside the room will be a blue cube. Be ready to get back into the main room quickly because once you take this cube, the water level is going to rise and submerge this entire wing. With the cube in hand, head back to the main room and Neloth will grab the first cube you used in this area to lower the water. This will raise the water once again and submerge the path to the exit. You'll have to swim under the platform with the three red pedestals to find the door back.
This will take you back into the Great Hall once more. When you get here, go up the ramp once. You won't go all the way to the top but instead will find yourself in an area with four large pump structures. At the base of each of these will be blue pedestals. Put a Cube on each of these. To do this, you'll have to remove one of the pedestals from the upper level. When all four cubes are in place, a Centurion will appear across from the four pumps and will come across a bridge that just lowered.
Kill the Centurion and investigate the room he came from for a chest. When you are ready, take the elevator up to the first level of Nchardak and hit the button that is now marked. Some lights will move around in the room and the book will rise up out of the center of the room. Read the book to continue.
