You'll want to go into your pixpet inventory and scroll to the bottom of the page! There's a thing there that says "add to pixpet market", and you can use that to sell it in auction. There's also the option to "release pixpet to the wild" (or something like that) that sells it back to the server instead of through an auction!

For future reference, you can also sell items in auction using the same steps in your inventory, and can sell back to the server using the sellback page under the item inventory!