Brenuin will tell the Dragonborn there is a rare bottle of Argonian Ale in the kitchen of the Bannered Mare and will ask for it to be stolen for him. The Ale can be found in the Bannered Mare through the left door inside the house (in the kitchen in The Bannered Mare). It is relatively easy to obtain — there is usually no one in the room, but if there is, it can be carried upstairs and taken there, where there are no witnesses. If the inn owner is a friend, the ale can simply be taken, and it will not be stolen. Any nearby characters will not respond with hostility, but some may say, 'That was just lying around? Nice find,' or something similar.
If you wish to keep the bottle of Argonian Ale for personal use, it can be stolen from Brenuin after the quest is completed. With a high enough Speech skill, it can also be sold to a shop vendor (or a fence, progress has been made into the Thieves' Guild), then re-buy it to negate its stolen status.