Start down the ramp but be careful as a couple of Cultists similar to those from Whiterun will be on their way up. Kill them and go through the door at the bottom.
You'll find yourself inside of Miraak's temple. There are several doors off of this main hallway with loot if you'd like but when you are done, go up this hallway. The hall will open to a room with a large face on the opposite wall. Just in front of the doorway as you're exiting will be a pressure plate. Jump over it to avoid the darts and continue on into the next hallway.
Kill the next couple of Cultists here. The next room will wrap around in a semi-circle and then open to another hallway. There are two more pressure plates in this room but if you pay attention and walk between the pillars, you can go right around them. At the end, turn left and pull the chain at the right of the gate to open it.
This will put you in a square room with a pit in the middle. Jump into the pit and make your way to the bottom. There are a few more cultists at the bottom and behind them will be a gate. Just to the left of the gate will be the lever to open it. In the hallway just after will be a path with a bunch of blue carpeting. The carpeting will lead the way through the hall but be careful because it will also lead you directly to a trap.
When you run out of carpeting, you'll see a spike door to the left and there will be a pressure plate not far in front of it. Hug the right wall to get past the pressure plates and then take either path ahead but move quickly because there are other traps that will trigger behind you. Both of them will lead to a double door.
Beyond the double door will be a long, wide hallway with lots of swinging blades. The goal is to walk past two blades and then stop in the archway. Each of these is a safe spot and there are always two blades between each one. Wait for them to swing by and sprint to the next one. You may be tempted to use your Whirlwind Sprint but it won't quite make it to the end so you're going to have to luck out on one end or the other if you do this.
On the far side of the trap, pull the lever on the right side to open the gate. The next section is a little bit confusing so try to follow along. Go through the double doors ahead and on the other side veer right just a bit. This will lead you between two walls and through a small doorway. Through the doorway, turn left and hug the left wall. This will lead you to a lever that will open the door directly across from it. Go through that door.
This will lead you to a wooden walkway with dangling tripwires ahead. You have to hit the tripwires to lower the drawbridge and get through the next room. When you go down the wooden draw bridge, you'll find a stone bottom and then three other draw bridges will open ahead of you. On the stone ground in between will be several pressure plates. If you step on one, it will activate the dart traps in this room, making combat a little bit tougher.
Several Draugr will come down the draw bridges on the far side of the room. Kill them and walk past them to find another set of double doors. Go through those to enter another section of the Temple.
Temple of Miraak Sanctum
Walk down the stairs and through the caged bridge. You'll come across a small army of skeletons but they should be of much lower level. Just beyond them will be a hallway with a couple of standing coffins and two Draugr. You'll also notice a couple of logs hanging from the ceiling waiting to swing down at you. There is a pressure plate on the ground between the coffins. The Draugr may get hit by the trap themselves if you're lucky.
Pass by the trap and go up the ramp beyond this hallway. Turn left and the cave will lead you to a large room that looks like it is in the middle of being excavated. If you have a higher level Whirlwind Sprint then you can hug the wall on the left, go down the stairs and then dash across the gap to the next platform. If not, hang to the right and go down the other set of stairs. When you proceed down the stairs, sprint because there is a pressure plate that will trigger another swinging log trap.
When you get to the next platform, turn left because a couple of Cultists will be coming up the long set of stairs. Kill them and make your way to the bottom of the stairs that they just came up. At the bottom, go left and you'll find a Word Wall where you learn the first word of a new shout called Dragon Aspect. When you do, the coffins in the room will open and start to deposit Draugr into the room. If you feel confident, deal with them now. If not, back up to the long stairs and this will give you some room to back track if you need it. Kill all of the Draugr and find the Gatekeeper. You'll find a key on him that will open the door hidden in one of the coffins (the one in the center of the room).
Go through that door and you'll enter a dining area. Go through this area and into the next. You'll find yourself in a small hallway but if you go left, you'll find yourself in an even larger dining room. Go to the opposite corner of the room to find a doorway leading out. In this hallway, hug the right wall. You'll pass a nook on the right and then come to another. In this second nook will be a lever. Flip the lever and you will open a door in the large dining area.
The next hallway will be pretty long and at the end, you'll enter into a room with a large metal cover in the middle of the floor. This room is otherwise empty but in the next room, you'll find a similar pit in the middle of the room. However, this time there will be a lever on a pedestal off to one side. If you hit the lever, the gate will open in the floor and you can drop down. Go down this stairwell and then down the next as well. You'll cross a couple of rooms with fire pits in the middle and enter another cave.
When you reach the end of this cave, look for another switch to the left of the flat cave wall. Hit the switch and the wall will move revealing another passage. Take the stairs down and go through the doors at the bottom. You'll enter a huge room with a large dragon skeleton statue in the middle. Walk up the stairs and along the room but be careful because there are Draugr all over this room. When you reach the top, you'll find a Boss Chest behind a large sarcophagus. Open the chest and then go past it to find a doorway hidden behind the wall. The doors will leave you in another small cave and when you come out on the other side, you'll enter a round room with a book in the middle. Pick it up and read it. It's time to meet your predecessor.