HT4895: Using your Apple ID for Apple servicesLearn about Using your Apple ID for Apple services
Currently Being ModeratedMar 15, 2013 2:08 PM (in response to Lysgar)
First decide which iPhone will be keeping the current iCloud account. On the one that will be changing accounts, if there are any photos in your photo stream that are not in your camera roll or backed up somewhere else, save these to your camera roll by opening the photo stream album in the thumbnail view, tapping Edit, then tap all the photos you want to save, tap Share and tap Save to Camera Roll.
Once this is done, go to Settings>iCloud, scroll to the bottom and tap Delete Account. (This will only delete the account from this phone, not from iCloud. The phone that will be keeping the account will not be effected by this.) When prompted about what to do with the iCloud data, be sure to select Keep On My iPhone. Next, set up a new iCloud account using a different Apple ID (if you don't have one, tap Get a Free Apple ID at the bottom). (Note: you can continue to share the same ID for purchasing from the iTunes and App stores; it does not need to be the same as your iCloud ID.) Then turn iCloud data syncing for contacts, etc. back to On, and when prompted about merging with iCloud, choose Merge. This will upload the data to the new account.
Finally, to un-merge the data in the two accounts you will then have to go to icloud.com on your computer and sign into each iCloud account separately and manually delete the data you don't want (i.e., deleting daughter's data from your account, and vice versa).