To start this quest, go to Solitude and from the entrance, go left and you'll find an Argonian outside Angeline's Aromatics called Jaree-Ra . He asks if you want to make some easy coin. He and his sister Deeja are Treasure Hunters, or so to speak. He'll tell you about a ship coming in and how if someone "accidentally" put out the lighthouse fire, loot could be had. Keep listening and soon the quest will start.
Leave Solitude from the main entrance and travel northeast to find the Solitude Lighthouse , where the marker is (its on the cape, naturally). Once there; go to the top and turn off the lights to complete the objective. You don't have to go inside the lighthouse's door to complete your objective, but you can find an ALTERATION SKILLBOOK named "The Lunar Lorkhan" inside if you do.
Beware of stealing it as the resident Khajiit man not be too happy. Now fast travel back to Solitude ( or the East Empire Company Warehouse ) and make your way back to Jaree-Ra (follow the marker).
He tells you to meet up with Deeja, who's at the wreckage. Swim across the sea until you reach Deeja, or better yet, until you get inside the Icerunner. There are no enemies, so loot what's left of the place and go to the bottom to find Deeja. Speak to her and she "betrays" you. Dammit. Kill her and loot her corpse to find a ' Note from Jaree-Ra '.
Once you read it, you know where to go. But it won't be easy, since you now have to fight everyone on your way back out. Leave the Icerunner and kill all the enemies here. Once outside, fast travel to the Lighthouse and move northwest to find Broken Oar Grotto . Once you get here, its time to get our payback. Kill the two enemies on top of the wooden structure.
When you reach a fork in the path, go left up the path and kill the enemy at the end (be sure to search the right path for a chest). Use the lever to lower the bridge. There's some stairs nearby that you can go down and find another chest inside a boat, but then go up and cross the bridge and you'll be at another fork.
Go inside the entrance (the right path takes you back the way you came), kill the two enemies in here, loot the place and continue. Once "outside", you'll see a boat with several enemies. Try using your bow to take them down ASAP. Now simply kill Jaree-Ra and the quest is over. Nice.
The Icerunner's chest is inside the structure, loot it as well as all the treasures in the place. You'll see a boat sunk on the left of the ship you're in. There's also a chest here. If you killed the captain and looted the key, then easily loot this chest as well. Loot the place clean, and be sure to grab the SMITHING SKILLBOOK "Cherim's Heart" from the smithing nook. This ends the quest.