From Nookipedia, the Animal Crossing wiki
The player can also sell his or her own belongings - any furniture out on the ground floor when villagers visit is up for sale. However, even if the player runs out of items to sell, the villager will take a few minutes to leave unless the player leaves, in which case the villager ask if the player needs to go, and say he or she should leave. If he or she leaves and re-enters the house enough, every villager will come in once.
Items or creatures that a villager buys from the house usually will be displayed in their house the next day.
Flea Markets are held usually on Saturdays, but if the player is ahead of a scheduled flea market (due to a time-warp) if the player time-warps back in time the flea market will be set to the next day (like many other events).
When the player is buying from the neighbors he or she can either take the price they give, or leave it. If one of them is buying from he or she however, they will haggle by saying the price is too high, and the player has to lower it for them to buy it. Comically, a cranky villager, when buying something from the player, may hand him or her money that the villager claims is from their super secret giant bell hoard.
A villager will buy a max of three items from the player's house. However, if the player goes into a different room without leaving the house, then he or she can go back to where the villager is; it resets it so that the villager will buy another three items. This can be repeated at the player's discretion. The maximum acceptable price the villager will pay is a little over twice the selling price to Tom Nook, which means for furniture, they will sell for half the buying cost. If the player has bugs or insects in the house, the same rule applies, twice the selling price. So if the player stock up on high priced fish/insects before or during a Flea Market Day, the player can make double amount of bells by placing them in the home and coaxing the villagers towards the creature the player wishes to sell.