IOS – “Verification failed” when trying to update to iOS 8.1.1 because of a network issue

One known condition for the install is that the device must have ~5GB free space for the temporary download of the installer file. You should delete unused apps, music and photos/movies from your iPod before you run the installation. The iPod should give you an error message saying the device doesn't have enough room.

Go into your iPhone's Settings. Select General -> Software Update. Here you can initiate an OTA update. (right now you will be placed in a waiting queue which could range from a few minute to a few hours due to demand).