Instructions
Play through the game until you reach the fourth Sunday in the current month. You will see the notice "Today is the Flea Market!" when it goes into effect.
Go into any of the other houses and talk to the owner. The owner will give you a greeting the first time that you talk to him. Talk to him again and he'll ask you if anything looks good to you. Say "Oh, yeah!" and look around the house or shop.
Click on the item in the house or shop that you would like to purchase. The owner of the item may tell you that it's not for sale, in which case you'll have to move on to another item. If the owner is willing to sell an item then she will tell you her suggested price. You can either buy the item at that price or pass on it.
Go back to your own home. Other citizens will stop by and offer to buy items from your home. When they find something that they like, they will ask you for a price. Enter in the price for the item and the citizen will either accept or reject the offer.