Hi,
On the Mac > System Preferences > iCloud you can sign out of one Apple ID that is used with iCloud and in with another.
In System Preferences > Mail, Contacts and Calendars you may also need to remove the Apple ID you wish to discontinue using.
On the iPhone similar thing can be done in Settings and then the various apps such as Messages, FaceTime iCloud etc.
9:27 pm Wednesday; January 1, 2014
iMac 2.5Ghz 5i 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad