This trick can only be done with a quest that allows you to select between two different items when you go to collect the reward. It cannot be done with quests where you have to pick between, for example, Claptrap and Hammerlock for the "Bullymong Fur" quest. It is nearly impossible to do this in single player mode. It does not duplicate the experience or cash reward, only the item (be it a gun, shield, relic, etc.). Complete any quest that lets you choose between two items in the quest reward screen. There are multiple ways you can go about this, but the main thing you need to know is that you have to fall into Fight For Your Life mode after pressing Back, which brings up the quest reward screen.
Duel the player that is going to turn in the quest. For example, assume they are player one. Player one talks to the person, bounty board, etc. and turns in the quest. However, do not choose the reward yet. Player two beats them down while they have the quest reward screen displayed. Player one will fall into Fight For Your Life mode and will have successfully stacked the quest reward. You can "stack" it as many times as desired by repeating the duel. Have player one press Back, and player two defeat them in the duel. At this point you would have three stacks. When you are done "stacking", press Back and you can select a reward as many times as you have stacked. When you choose an item, the quest reward screen will appear again repeatedly until all the stacks are used. Player two can also do this, but it may only work for a single player at one time.
If you are the player that did not turn in the quest you can run into a group of enemies and press Back to bring up the quest reward screen then let them push you into Fight For Your Life mode.
This is an easy way to get the White, Green, Blue, Purple, Orange item pick up challenges, and getting money from selling the more expensive items.