Using this dialog, you can request coins from another person (who should already have installed Bitcoin Wallet).

First, you can enter an amount of Bitcoins to request.

Then, you either have the generated QR code scanned by the other person. Or, you can send your request to a remote person with the share button in the action bar. The other person will have to click the Bitcoin URL.

Either way, the other person will be presented a dialog for sending coins with all fields pre-populated. If she accepts, all she needs to do is sending the transaction.