This quest is given by Delvin Mallory . "Fishing" is just HIS way of saying " Pickpocketing ", so for this job you will be tasked to take a RANDOM item from a RANDOM person throughout Skyrim, so as you can see you may end up going to a number of places.
There’s two things to know about pickpocketing. The first is that your mark will OFTEN be walking around out in the open. This means that you’re going to need to TAIL them while sneaking so you can pickpocket them. Be SURE that you are HIDDEN before doing the actual pickpocketing. The second thing to know is that pickpocketing is all about percentages. The item you are sent to get may have a very low percentage of you being successful, so be sure to SAVE first and foremost, and then equip as much " Deft Hands " ( + Pickpocket Skill ) gear that you can!
Once you have the item in hand, return to Delvin and let him know. You will be given your cut (400 Gold) and the job is complete.