Non-spoiler solution copied from my Solution for House of Sorrows in Kingdoms of Amalur: Reckoning
The House of Sorrows is the only faction not available on the beginning (West) side of the map. In order to access the East side of the map, you must beat the Balor at the Battle of Mel Senshir:
and you must defeat Octienne in Adessa:
After those victories, most of the Eastern map becomes available, and you will be able to leave Mel Senshir through the Southern exit.
When you leave Mel Senshir, travel East, through Cursewood and towards The Midden. You will find a Fae named Bisarane sitting cross-legged in the path between the areas. Offer to help him and he will send you to the Proving Halls, which will start the House of Sorrows questline.
The quests in this questline are:
•The Sorrows Call
•Voices of the Dead
•A House Divided
•The Weeping King
•Such Sweet Sorrow
Please ask questions in the comments section and I will expand the solution if needed.