How do one back up when the storage is full?

If your iCloud storage is full, you cannot put anything new there, including an updated or new backup. You would have to delete iCloud content to clear our space, or subscribe for more iCloud storage.

You can always backup to a computer using iTunes or finder.

Hello ~Take a look here and remember we are fellow forum users like yourself and need time to locate and post helpful information:

If you can't back up to iCloud - Apple Support

~Katana-San~