If you are having trouble finding the Airplay button, keep in mind that the AirPlay button will only show when another source (Airport Express/Apple TV) is available on your current network. You can find the AirPlay button in a couple of different places:
If Pandora is actively playing but not the currently open window, double click the home button on the device. Swipe to the right along the area at the bottom to reveal the music player controls and Pandora icon. Tap the AirPlay button (to the right of the forward button) and select the other source you want to stream to.
If Pandora is the active window on your device, then you can slide up the volume bar by tapping and moving up the three lines that you see near the bottom of the screen (they are located between the thumb up and the pause/play button). You should then see the Airplay button to the right of the volume bar. Tapping on this button will also allow you select the other source that you would like to stream to.