Beginning the Quest
When you're ready to begin your first major quest out in the lands of Amaranthine, speak with Varel in Vigil's Keep throne room. He tells you that one of the Grey Wardens, Kristoff, has been away tracking down a lead on why the darkspawn were still active after the Blight. The seneschal believes Kristoff can be found in the city of Amaranthine. At the conversation's conclusion, you gain the "Shadows of the Blackmarsh" quest.
Amaranthine
When you enter Amaranthine, look for the Crown and Lion Inn in the city's eastern section. Proceed north by Constable Aidan and turn right at the intersection. Climb the stairs and the Crown and Lion entrance is on your left (just before you turn for the steps leading up to the Chantry). Inside you'll find a clue to Kristoff's whereabouts.