In the ‘Buying’ tab, you can browse all sell offers currently available. You can narrow your search by using the various filters/search functions available to carefully plan who you’d like to place a bid on.

Tapping on a sell offer brings up details (including time remaining and bid history) and the bidding interface.
Where there is an ‘instant buy’ price, you can tap to attempt to claim the sell offer there and then. If another user has claimed this purchase before you, you will be notified that the trade cannot take place.

To take part in an auction, you can place a bid higher than the current highest bid (as long as you can afford it). When you place a bid the coins are taken from your account and held in escrow by the game until the bid is superseded or the auction is won.