To receive bitcoins, just show the QR code shown on the main screen to the person sending you coins.
If you wish to specify an amount to receive, or request a payment over e-mail or some other means, press the «Receive» button, press the keyboard button to enter an amount, and press «Share Bitcoin Address» to select a method of sending the request. The list of methods will depend on the apps you have installed on your phone. You can switch between entering the amount in bitcoin, or in your local currency, by pressing the mBTC button in the top right corner next to the amount being entered.
This lets you request an amount in bitcoin equivalent to a specified value of your local currency. The currency and exchange rate used here is the same one you select to be displayed on the main screen.