The Legerdemain Skill line can be increased by Picking Locks, Pickpocketing, and Fencing/Laundering Stolen Goods.
If all you intend to do is steal from containers and Fence and Launder goods it will take a long time to lever this skill line to 20. What I did was check to see how much experience is give for Picking Locks, Pickpocketing and Fencing/Laundering items, the breakdown is as follows:
Fencing and Laundering Items: 1 item = 1 exp point (Doesn't matter whether the item is white, green or blue)
Pickpocketing:
Easy: 1 item = 1 exp point
Medium: 1 item = 2 exp points
Hard: 1 item = 4 exp points
Picking Locks (Doors and Boxes)
Simple = 1 exp point
Intermediate = 2 exp points
Advance = 4 exp points
Good Luck