Outside the Box
You'll receive this quest after completing the mission "Mirror, Mirror". Its description can be found in Plains of Erathell guide.
First head to the Sun Camp M5(7) and talk to Argine, who lives there.
She will send you to a local Hierophant shrine, where you'll receive a mission to steal the master's pick. It is in possession of Eloren Criet in Adessa.
You'll find her in Laboratories M5(9).
Talk to her and use gold or persuasion to get information on the item you're looking for. It turns out that it was taken to the armory M5(7).
Only guards can stay inside the building, so use sneaking once you get there. A box with pick can be found at the back of the location. You can also run there quickly, pick up the item and pay a fine for trespassing.
Unfortunately the box is locked and you'll find only a note next to it. Bring it back to Argine in Sun Camp M5(7).
The woman will send you to the Motus Mining Headquarters M5(5). In undergrounds you will find a mechanism which can unlock the box. Use it and then take a damaged pick to Argine.
This task becomes available after completing the mission "Outside the Box".
First talk to Argine in Sun Camp M5(7) and then pray at the Hierophant's shrine.
You'll be sent for a meeting with Maun Cointaker, who can be found in Convict's Cavern M5(10).
Break in and talk to the man. He will give you one of three key to his treasury in Snaketail Grotto M5(8).
Map of Snaketail Grotto
1 -Maun Cointaker's treasury
2 - Chest with a key
Inside you'll see two groups of bandits fighting with each other. Kill all opponents and then collect two other keys.
In one of the chests you'll find Zungar Key and in other - Darkvari Key. Use them to open the thief hideout.
But you won't find anything valuable inside. You'll find only a letter, which you have to bring to Argine.
But instead of getting back to Sun Camp, talk to Grim Onwig waiting next to the exit from underground. He will give you another quest.
The Purloined Letters
This task becomes available after completing the mission "Classic Misdirection"
Grim Onwig will ask you to steal some book from undergrounds of Livrarium in Adessa M6(14).
Go there and meet Phasmer Humm. After short conversation the man will show you a descend to the basement, located in the floor.