Trading is a feature of the game, in which players can trade mature, tamed frogs with any neighbor on the Game Center/Mobage network using stamps.
You must be logged in to the Game Center or Mobage to send or recieve a frog. One stamp will be deducted from the sender's stamp total when they choose to send a frog. The recipient does not need to be logged in at the time the frog is sent, they will recieve it upon their next log in. However, the recipent must accept the sender's friend request before they or the sender can send or recieve a frog. It does not cost a stamp to recieve a frog, only to send one. Frogs must be tamed in the pond before they can be gifted to another player.
To trade frogs, you must have a Game Center ID (Mobage for Android), the Game Center/Mobage ID of the player you wish to trade with, and the sender must have at least one stamp. The sender must add the recipient to their 'Neighbors' list by searching for them in the Game Center network. Opening the Pocket Frogs menu and selecting 'Game Center Network' will open the sender's profile view. There, under the Friends tab, is a yellow button with the words 'Find Friends' on it. By selecting 'Find Friends' you now have the option of searching a wide variety of networks for people you wish to add. If you select 'Search Game Center' you will be able to input the recipient ID or email and they will be added to your 'Neighbors' list.
After you have the recipient added to your 'Neighbors' list you must then select the frog you wish to send. Tap on the frog in habitat view to bring up the frog menu. Assuming the frog is tamed, an option to 'Gift' should appear in the menu. Selecting 'Gift' brings up a list of people you have added as possible recipients. Select the player you wish to trade with and a window will pop up prompting you to validate the transaction.
After a frog is sent it will be removed from your habitat and one stamp will be deducted from your total. There is no way to retrieve a frog after it has been sent. A player may clone another from their froggydex, request another in the forum, or request it back from the recipient however there is no method of direct retrieval after it has been sent.
You must be entering the app in order to recieve a frog. Until that time, it will simply hop around the Game Center server waiting for you to trigger it. Frogs recieved will be sent to your mailbox and are subject to the same delivery rules as presents found in the Pond.