Check the range of the mobile network, see this Apple article:
If you see No Service or Searching on your iPhone or iPad
If you see No Service or Searching on your iPhone or iPad - Apple Support
Check Wi-Fi network, see the following Apple articles:
Connect to Wi-Fi on your iPhone, iPad, or iPod touch
Connect to Wi-Fi on your iPhone, iPad, or iPod touch - Apple Support
If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network
If your iPhone, iPad, or iPod touch won't connect to a Wi-Fi network - Apple Support
You can do the update via PC, see this Apple article: Update software on iPhone, iPad or iPod touch in iTunes on PC
Update software on iPhone, iPad or iPod touch in iTunes on PC – Apple Support (UK)
If you have a Mac see this Apple article: Update your iPhone, iPad, or iPod touch with the Finder
Update your iPhone, iPad, or iPod touch with the Finder - Apple Support