The first thing you may want to try out is changing the update method. If you are trying to do the task wirelessly, do it by using iTunes. If you have been using iTunes when the issue appeared, try updating your device wirelessly.
The network timed out issue often appears when the Internet connection is poor. Restart your modem and your router, and try again.
It is crucial for you to have the latest version of iTunes. If the update step does not fix the problem, uninstall the software from your computer, and install it again.
If the firewall is enabled, issue such as network timed out may happen. However, once you put it out of action, there is a huge change that everything will work just fine.
Another solution is to disable your antivirus software, since they often block the update, causing all kinds of issues.