Skyrim:Hired Muscle

Quick Walkthrough
# Speak to the assigned target.
# Brawl with them to send a message, but don't kill them.
# Return to Farkas.

Detailed Walkthrough
:Note: it is best to complete this quest as soon as possible after receiving it, because many of the quest targets can possibly die (either through random or scripted events), at which point it becomes impossible to ever complete the quest or take any other jobs for the Companions.
Farkas will send you to rough up one of over 400 different NPCs, encompassing nearly every citizen in Skyrim.  The NPC will be located in a hold that you have previously visited, so early in the game you may only be given NPCs living in Whiterun Hold, but later in the game there are many more possible options.  The NPC may live in a city, town, or a remote settlement.

Once you have traveled to the target's location, talk to them and select the dialogue option to brawl with them.  It is best to start the brawl in an area with as few other NPCs as possible.  In particular, it is best to have any follower wait in a different room.  You may not use any weapons, magic, or shouts during a brawl (but using spells such as Fear or Oakflesh before the fight is permissible).  If anyone else becomes hostile as a result of your brawling, you should be able to run to a guard and yield, clearing any hostility.

If you kill the target, you will still complete the quest.  The quest is marked as "Failed" in your quest journal, but it is no longer active, and you will be allowed to pursue other jobs in the Companions questline.  Farkas will not be pleased, and you will receive a decreased amount of gold for your reward.

Return to Farkas for a gold reward.

Reward
 

Notes
 
If your target is someone you can fight for money, you can collect a reward from them after the fight, even if you've already won a bet with them previously.
If your target is someone you can brawl for another quest (such as Mikael), winning a brawl will complete the objective for both quests simultaneously.
There is a silent Intimidate check against the target as part of the quest's startup conditions. If it succeeds, you won't get the quest.

Bugs
 
Check whether you have quests from other Companions Council members and try completing those first. E.g. "Stealing Plans" from Aela will hinder you from completing "Hired Muscle".
 
You can reload a save before taking the contract.
 Type   into the console.
 
Assault the target and then run to a non-trespassing location out in public, where the target will follow you. You can then yield by sheathing weapons, calm the target by using the Voice of the Emperor power, pay the fine for assault, or go to jail and hurry back to the target.
 Use the console commands   and your target's RefID, then   to move the target to you, and the brawl can be initiated without committing a crime. 
You may clear the quest from your active quest list by killing the target and thus failing the quest. After killing the target, return to Farkas and he will give you a lesser amount of gold for your payment before allowing you to take another job.
 
   
 Typing   into the console will allow you to skip the intimidation step and complete the quest.
 
 
You can escape combat with the guards and un-equip the Ebony Mail, then return to the settlement and pay the fine, or go to jail, but only if you haven't reloaded the game.

Quest Stages