When it's your turn to sling, you may first select which bird to use (unless there's only one kind left in the level) on your mobile device. Then you drag and sling using the slingshot on your mobile device. Please take a look at the main game screen to see how the slingshot there reflects your actions on your mobile device.

Release to sling, and tap on the big red button that appears to activate the bird's extraordinary power (if it has one).