The Auction House is one of the ways to sell your Pokémon to the highest bidder, there is a small transaction fee when selling through this method.
To begin auctioning off your own Pokémon, click "Hold Auction" Simply decide which Pokémon you wish to sell and how long you would like the auction to be. (1-5 days)
To bid on another players Pokémon, click on "Place Bid/Details" and enter how many coins you are willing to pay for the Pokémon. Remember you need to bid at least 1 coin higher than the previous bid!
Unsure how much something is worth? Take a look at the forum thread: https://pkmnreborn.com/forums/viewthread.php?id=406
While the above forum is just a guideline, you can always sell for more or less than the rate list.