You can get a free house after completing a series of side quests. The first of these is called 'March of the Dead' and is acquired from the town Guards captain, Captain Veleth, just outside and south of Raven Rock at a location called 'Old Attius Farm' when you save him from being killed.
The second required quest is called 'The Final Descent' and is acquired from Crescius Caerellius who can be found just inside the entrance of Raven Rock Mine. The mission takes you through the mine, so you can start it immediately upon acquiring it.
The third and final required mission is called 'Served Cold' and can only be activated once 'The Final Descent' has been completed. This too is acquired from Captain Veleth, who then sends you to one of the towns councilors to start the mission.
the reward for this final mission is a property in Raven Rock and upon receiving this reward, the achievement will unlock.