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This is easy. Once Tribunal is installed, find a nice place to rest, and go to sleep for a bit. You'll be interrupted by up to a couple of formidable Assassins nearby. If you search the body after they're killed, you'll find an odd looking dart. Find any guard and report the assassination attempt. If you then attempt to rest before the matter is taken care of, you'll have to deal with more Assassins... every time you rest.
The guard tells you that the attack looks like an act of the Dark Brotherhood and suggests that you speak with Apelles Matius in Ebonheart to learn more. (The fastest way to Ebonheart short of a Recall spell is to buy a teleport to the Vivec Mages guild, go outside and to the northeast end of the building, jump off using a slowfall enchanted item or potion or jump into the water, and use the boat nearby.)
You'll find Apelles Matius walking the battlements on the southern end. He'll tell you that the Dark Brotherhood has a large contingent in the capital of Mournhold and to speak with Asciene Rane in the Grand Council Chambers about transport there.
Step inside the southern most building and you'll see Asciene Rane on the right side as you enter. Speak with her and she'll gladly transport you there, but not before telling you to speak with Effe-Tei and then a guard in the Royal Palace once there.
You're now officially in the Mournhold Royal Palace Reception area. Effe-Tei the Argonian is there in the room. Speak to the Argonian and then speak with a guard, and you'll learn that the Dark Brotherhood operates out of a base accessible from the sewer system underneath the Great Bazaar.
You can immediately attempt the quest, but my suggestion is, now that you can rest without fear of sleep-interrupting attempts on your life, have some fun by exploring and learning the layout of the city. Perform some miscellaneous quests in Godsreach or the Great Bazaar, and visit the Temple. You'll find more quests there from Fedris Hler.