If you want to upgrade Coppermine installed from Fantastico, just follow these steps:

Go to cPanel --> Fantastico --> Image Galleries --> Coppermine --> Find your current installation and click 'Upgrade'

If there isn't any 'Upgrade' button/link, that means that the application is up to date and Upgrade is not available.

If your Coppermine is not installed through Fantastico, or you particularly want to upgrade your installation manually, you can read this detailed tutorial for more information on how to manually upgrade Coppermine.

Please note that manual upgrades can cause database corruptions, data loss and break you script's functionality. You should always make a backup before upgrading an application.