How do you get data out of iCloud?

Depends on how it got there.

If its backup of an iOS device, then you need to restore the backup onto another iOS device: Restore your iPhone, iPad, or iPod touch from a backup - Apple Support. or follow the steps in the support document you posted from.

If you were using iCloud Photos, Music Library, Contacts, Notes and Calendar, then signing in to the relevant Apple ID at https://icloud.com will let you access that data. Same thing for files in iCloud Drive.

Alternatively, you can simply sign in to the related Apple ID on a new iOS device and turn on the iCloud features in Settings->Account (top of settings)->iCloud to sync all thew data down to the new device.