Some information I lifted from Herodotus' The Histories (and other sources):
The earliest auctions in recorded history happened in ancient Babylon. The Sumerians traders used construct special boats made out of wooden frames that was then lined with animal hide. The traders filled up the boats with their merchandise and also take a couple of mules or donkeys before sailing downstream with great ease. As they reached their destination they sold the merchandise and then took the boat apart and held an auction to sell the wood from the boat's frame. Finally, they packed up the animal hides on their donkeys and travelled back to gather merchandise for their next trip.
The more famous auctions of Babylon took place in the villages where every year the marriageable maidens of the village were gathered next to a platform and men from all walks of life bid to find their brides. The most beautiful maidens were auctions for marriage first, and given to the grooms who was willing to pay the most to the public pot. Once maiden was won in marriage she was led down, and the next most beautiful girl came up on the platform.
Then there was this famous auction in 193 AD where the Roman empire was put on the block by the Praetorian Guards after emperor Pertinax was murdered. In what could be giving a new meaning to the phrase "winner's curse," the winner of the auction Didius Julianus was killed shortly thereafter. Just like in the Babylonian days selling items through auctions has been common throughout history. The Roman soldiers, for instance, routinely auctioned off items that were looted and brought back from conquests.