Go to Settings, iCloud and switch all of the "On" buttons to "Off" (but OK to keep Find My iPad switched on) and select "Delete from My iPad" for each of the buttons you switch to Off. You'll want to delete so that when you log back on the data will be updated with the new data.
Then at the bottom of the screen select "Delete Account", and click "Delete" again and then again.
Now you will have a new iCloud screen where you can type in your Apple ID and password.
This works for iPhone too.
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