(1) Exit the throne room area and enter the courtyard. Before you leave for the lands outside the keep and embark on any of the main quests, you need to pick up one more companion. When you leave the throne room, the private at the gate hands you two letters that open up the side quests "A Daughter Ransomed" and "Far Afield."
See the Side Quest chapter and follow up on them when you have a chance. Once you complete these two side quests, you can return to the private for one more, "Salvage Operation." The private also tells you that the keep guards have a prisoner in the dungeon. It's the prisoner that you want to see.
(2) Descend into the dungeon and ask the dungeon guard to let you see the prisoner. The man behind the bars is Nathaniel Howe, son of Arl Howe, who plotted against the Grey Wardens with Loghain in Dragon Age: Origins. If you imported your character, you may even be Arl Howe's murderer! Nathaniel wants nothing to do with you at first, but you sense a good heart in this rogue's body.
Call the seneschal and conscript Nathaniel Howe into the Wardens. The next time you return to the throne room and speak with Varel, Nathaniel survives the Joining and becomes a Grey Warden.
(3) With Nathaniel Howe in your party, head to the eastern section of the courtyard. The groundskeeper Samuel walks by and Nathaniel recognizes him. Samuel tells Nathaniel that his sister Delilah is alive, and he gives you "The Howe Family" side quest. While you're in the area, pick up the stray cat that meows along the far buildings. The kitten is actually a gift for Anders.
(4) Level up your characters. Buy and sell at the vendors. Add runes to your more powerful magic equipment. When you've completed all that and finished off any Vigil's Keep side quests that you want to tackle at the moment, head out the gates to the world at large. It's time to journey to Amaranthine and tackle your first major quest.