HT4895: Using your Apple ID for Apple servicesLearn about Using your Apple ID for Apple services
Currently Being ModeratedMar 14, 2013 5:33 PM (in response to Stuart P Myers)
Go to Settings>iCloud, tap Delete Account, the sign back in with the new ID. This deletes the account and your synced data from your phone, but not from iCloud. Provided you are signing back into the same account, your data will be synced back to your phone when you sign back in. However, if you are changing to a new account, choose Keep on My iPhone when Prompted. Then choose Merge when you sign into the new account to upload your data.
Prior to deleting the account, if you have any photo stream photos that you want to keep, save them to your camera roll (tap Edit, tap all the photos, tap Share, tap Save to Camera Roll).