This quest begins automatically upon arriving at the Shadow's Edge, and more specifically - the moment you reach the [Tree of Death]. Traditionally, start exploring the place after talking to Crowfather.
[TIP: Same as with other locations, don't worry about the Shadow's Edge being a completely cut off area. There are portals here which lead to the previously explored places in the game.]
Head north. This particular location isn't too large, so you won't need the area map for the moment. Your goal is the entrance shown on the screen, which leads to a small dungeon. You need to go through that dungeon in order to reach your proper destination.
Head north, and after reaching a fork in the road (the one with a Serpent Tome) take the left corridor. Stop at where the screen illustrates and use the interactive edges on the right to get to the upper balcony. Look around for a Book of the Dead page ([The Book of the Dead] side quest).
The Serpent Tome mentioned above isn't the only secret hidden in the dungeon. Have Death stand on the pressure plate seen on the screen and activate Soul Splitter.
Take one of Death's halves to the fork passed by before (Serpent Tome) and go through the newly unlocked passageway on the right (the above screen) - this will take you to an east room holding a Relic of Khagoth ([Lost Relics] side quest).
Deactivate Soul Splitter, jump down and run towards the dungeon's north exit. Right after leaving the dungeon you should meet Ostegoth again, and apart from using up all dialogue options trade with him as well.