How to Trade Properties in Monopoly for iPhone

In "bird's-eye" view mode (looking at the whole board):

1. At the bottom of the horizontal screen, you will see a number of square buttons. If you have not already rolled, you will see a some dice.
2. You should also see two deed cards (they actually look more like old-school wheel iPods) with red and green arrows facing each other. Tap this button.
3. If there are more than two players, click the icon of the player you want to trade with. Then tap the green checkmark button. 
4. Now you are able to tap that players cards, and view them up-close. Tap the one you want.
5. Tap the card once more, once it is already shown close-up. This will select it, and you will see a green checkmark in that card's upper-right hand corner. To deselect, just tap it again.
6. Tap the green checkmark button at the bottom of the screen to exit close-up view. 
7. Continue doing this for any other properties, and money trades. You can select more than one property per trade. 
8. Once you are finished, tap the green icon on the bottom of the screen, with the hand holding a deed card (looks like a calculator.)
9. If you are trading AI, you may choose to offer more if they decline your first offer. 

Tip: Be very careful in this screen! It is possible to give your property away for absolutely nothing by forgetting or simply not entering any $ or card value for the other player. Also, beware of "fat thumbs" - make sure to confirm whether it says "decline" or "accept" when doing either action from another player's offer. Those two action buttons are very close to each other.