You'll receive this quest after your first encounter with Varric. Your task here is to talk to him inside The Hanged Man. You can find The Hanged Man in the middle part of Lowtown. 

You must first find your way into The Hanged Man in Lowtown. Inside ,initiate a conversation with  your  companion Varric. In this cut-scene Varric will express the need of a better entrance to the Deep Road. Your first set of dialogue options has no bearing so you may choose whichever you like. After that he'll mention his new information about a Grey Warden in the city. Here is the list of you dialogue options and their respective companions relationship results.

Investigate - Choose this to ask more questions about the information he received about the Grey Warden or other way into the Deep Roads.

After the sequence of conversation you'll complete this quest and update your quest The Deep Roads Expedition. You will also gain a codex entry The Grey Wardens.

MAIN PLOT UNLOCKED -  Tranquility

RUMORS UNLOCKED -  Wayward Son

RUMORS UNLOCKED -  Act of Mercy

RUMORS UNLOCKED -  Enemies Among Us

RUMORS UNLOCKED -  Shepherding Wolves

If this is your first time in The Hanged Man, You may explore the area for additional loots and codex entry.
(1) Crate, (2) History of Kirwall: Chapter 1 - codex entry, (3) Crate , (4) Barrel

To acquire this quest you must first go to the Viscounts Keep. Upon entering take the left stairs then follow the corridor that leads to the room to the westernmost part of the Keep. You can acquire this quest by taking the bottle on top of the office table. 

You'll received this quest after your first encounter with Varric. Just after you finish the The Destruction of Lothering quest. Your task is to talk to Aveline who has been working as a city guard for the past year.

First find your way into Hightown. From there, Go to the most southern part of map. Note that you can only get inside the Keep during the day. You'll find her standing by the corridor of the City Guard Barracks on the southern part of the Keep.  Here you'll discuss her life as a city guard. Eventually she'll offer you a job. Its up to you to take the offer or let the guards do their jobs. Accepting it will unlocked a  new Companions Quest. Either way, she'll join your party and that will complete the quest. Additionally, You'll receive a Aveline Vallen codex entry.

If this is your first time in the Keep you'll find several codex entries, a locked chest and an additional sidequest. (1) Heirarchy of the Circle - codex entry, (2) The Llomerryn Accord - codex entry, (3) The Enigma of Kirkwall - codex entry, (4) Bottled Scar 5:34 Exalted - sidequest, (5) Locked Chest - Standard, (6) Chantry Hierarchy - codex entry, (7) The Kirkwall City Guard - codex entry, (8) A Study of the Fifth Blight, Vol  1- codex entry, (9) Locked Chest - Simple

COMPANIONS QUEST UNLOCKED : The Way It Should Be. 

To complete this quest during Act 1, you have to go to your Uncle Gamlen's Home in Lowtown  and enter the southern room. During Act 2 and 3 you can find it in the northern room in Hawkes Estate in Hightown. From there you can find a chest marked as Aldenon's Heirloom containing multiple items that includes the following chestpiece (Robes of the Pretender and Aldenon's Vestments). The following helmets (The Helm of Marterel and Wisdom's Eye). The following gloves (The Elusive Gloves and Gloves of the Winter Crossing). The following boots (Quickflight and Stalwarts Treads). A staff named Freedom's Promise, An amulet named Sylaise's Favor, a ring named Grandmother Amell's Wedding Band and a belt named Visionary's Girdle). Upon taking these items, you'll complete this quest and receive four codex entries (Aldenon's Vestements, Freedom's Promise, Robes of the Pretender and Wisdom's Eye).

 

 

To complete this quest during Act 1, you have to go to your Uncle Gamlen's Home in Lowtown  and enter the southern room. During Act 2 and 3 you can find it in the northern room in Hawkes Estate in Hightown. From there you can find a chest marked as The Apostate's Legacy containing multiple items that includes the following chestpiece (The Fugitive's Mantle and Malcolm's Bequest). The following helmets (The Fugitive's Crown and The Apostate's Mask). The following gloves (The Fugitive's Gauntlets and Black Silk Gauntlets). The following boots (The Long Trek and Orlesian Silk Boots). The following amulets (Ring of the Awakened and A Private Memento). A staff named Malcolm's Honor and a ring named (The Inner Eye). Upon taking these items, you'll complete this quest and receive four codex entries (The Long Trek, The Fugitive's Mantle, Malcolm's Bequest and Malcolm's Honor).