Getting Started
After loading up the DLC, visit Whiterun and as you walk in the front gate, you'll be approached by a couple of strange people wearing masks and robes. If they don't appear, level up a little or progress further in the main quest. When they appear, they'll first talk to you but no matter what option you choose, they will attack. Kill them both and check the leader's body to find orders. Read the orders which will direct you to go to Windhelm's docks.
Fast travel to the stables outside of Windhelm and cross the river to the docks below. Find Captain Gjolund Salt-Sage on the center boat (called the Northern Maiden) and after either paying him quite a bit of money or persuading him, he'll take you to Solstheim.
Solstheim
When you get to Solstheim and get off the boat, you'll be greeted by the Dark Elf Adril Arano. Question him a couple of times about Miraak and he'll direct you to the Earth Stone nearby. Walk around the port and up on a large hill will be a large stone sending a green beam of light into the sky.
As you approach the Earth Stone, you'll bump into Neloth. After talking to him some, you'll find out the Miraak has been dead for quite some time. He will give you your next lead however and send you up to Miraak's temple.
Make your way out of the town and up to the top of the mountain in the center of the island. When you get closer, you'll start to hear people working on the stone around here. You'll find Miraak's huge temple nearby. Climb up and at the top, go down into the round area in the middle. You'll see another large stone that looks like the Earth Stone. When you investigate, you'll find that it's called the Tree Stone. If you activate it, something interesting will happen.
Near this stone, you'll find a woman named Frea who is wearing a whole lot of armor. She'll be the only other person here who isn't working on the temple. Talk to her and then a path down into the temple will open.
