Why would you need to? IPCop's an appliance that runs 24/7. If you want to turn it off, navigate to the System>Shutdown page and hit the Shutdown button.
Periodically, fixes are issued to plug security gaps, fix bugs, or add new features. Keep an eye on the Home page, or the System>Updates page for alerts. Study the information and follow the instructions for downloading fixes to your Client PC, and then upload them to IPCop.
More information can be found in the System Section of the Administration Manual.
You can backup your settings to a floppy (or from v1.4.0, you can do it over the network). Using a floppy disk makes reinstalling or upgrading very easy.
Refer to the System Section of the Administration Manual for more information.