If you ever need to know, or ever have to help someone else, here is a list of steps to take to delete old iCloud backups and free up space on your various Apple mobile devices:

When a device is set to backup to iCloud, Apple automatically backs up data and settings stored locally on the particular device; it does not create a backup of data already stored in an iCloud account via Mac or iOS apps (as of iOS 8.1, that includes iCloud Photo Library, shared photo albums, My Photo Stream, documents, contacts, calendars, mail, bookmarks, and notes). iCloud backups include purchase history from the iTunes or App Store, app data, home screen and app organization, iMessage/SMS/MMS text messages, device settings, and visual voicemail on an iOS device.

The problem is, if users have multiple devices, old iCloud back-ups can quickly fill up their storage — particularly if they’re on the free 5-gigabyte tier.

This is a good link to keep handy just in-case. I have used this so many times that at this point the steps are committed to memory.