When you're just minding your own business, you might get attacked by a group of cultists. Once you defeat them, you should find a letter on one that will start the quest and tell you how to proceed.
Or you can just go to the Windhelm docks and talk to Gjalund, and he can take you to Solstheim. I believe you still need to be attacked by the cultists in order to start the quest and have it show up in your journal though, but they'll find you whether you're in Solstheim or Skyrim, so just hang around towns and cities until they show up.