How can I deactivate iCloud from my old iPhone?

iCloud: Change iCloud feature settings - http://support.apple.com/kb/PH2613 - for iOS, MacOS, Windows

"Turn off iCloud completely

Depending on whether you want to stop using iCloud on all or only some devices, do one or more of the following:

On your iOS device’s Home screen, go to Settings > iCloud, then at the bottom of the screen, tap Delete Account.

Note: If you delete your iCloud account, iCloud will no longer back up your iOS data. You can still back up your device in iTunes (for more information, open iTunes and choose iTunes > Help)."

Your granddaughter needs to do the following steps, one at a time

and allowing each step to complete before going onto the next step.

Then check to be sure Activation Lock no longer shows as active/on.

before sell/give away iDevice: https://support.apple.com/en-us/HT201351

She can use the same AppleID on her new iPhone as was used on her old

iPhone.

After all the steps are done, check the Activation Lock status here:

https://www.icloud.com/activationlock/

how to find serial number, IMEI, etc (see the section about if

you don't have your device since it is dead)

http://support.apple.com/kb/HT4061?viewlocale=en_US&locale=en_US

Settings -> iCloud -> Sign Out (Delete Account)

FYI, signing out deletes the account locally, but it does not delete the account, it will still be there if the user signs back in.