To begin this quest, head to the Frostback Mountains and gain entry to Orzammar. When you have to choice of whom to support to become the king, do the quest for Bhelen. Follow the line of quests that you receive for supporting Bhelen. Eventually, this quest will become intertwined with "Anvil of the Void." See Liberator and Pragmatist for more details.
After completing "The Anvil of the Void", return to Orzammar and choose Bhelen as the king of the dwarves. Despite doing quests for Bhelen, you will be given one last chance to change sides.