Pandora recommends restarting your device if you're having trouble streaming its radio service on iOS. You might also want to make sure your device is capable of running Pandora. The Pandora Radio app requires iOS 5 or later to work. You can follow these steps to find out what version of iOS your device is running:
Navigate to Settings > General > About and scroll down to "Version." This will let you know what version of iOS your device is running.
You can also try uninstalling and re-installing the app. Just hold the Pandora icon until it wiggles and hit the x to uninstall, and download it again from the App Store.