On the iPhone & iPod Touch
The Pandora app for the iPhone and iPod Touch has a sleep timer you can set to make your station stop playing automatically after 15, 30 or 60 minutes.
From the “Now Playing” screen, tap the button in top right of your screen to open up the Menu.
Then tap Sleep Timer and select how many minutes you'd like the timer to wait before it pauses your station.
If you do not see the sleep timer option, you may want to update the Pandora app as long as you are not running iOS 4.3.5 or below.
On the iPad
Pandora for the iPad does not have the same Sleep Timer feature at the iPhone/iPod Touch version.
If you are running iOS 6 or above on your iPad, you can use the Sleep Timer in the Clock app to put Pandora to sleep after a certain amount of time:
Tap the Clock app
Select a time
Tap When Timer Ends
Tap Stop Playing
This will sleep your Pandora app if it is running.