To put piglets up on sale in auction, tap on the "Auction" button on the popup which comes up when you either buy a piglet or when a baby piglet is born.
Piglets cannot be put up on sale once they are put in the Pig Pen or on the waiting list. Event pigs (marked with blue rarity ★'s) cannot be sold in auctions, either.
Bids can be placed for 24 hours after a pig has been put up for auction. If your pig is successfully sold, the points will be added to your account. If no one places a bid for your pig, it will automatically be sent to the Pig Pen if there is space. If there is not, it will be moved to the waiting list. Pigs on the waiting list will be moved to the Pig Pen automatically when there is space.