Currently Being ModeratedMar 15, 2013 3:56 PM (in response to michaelfrompicayune)
If the replacement phone isn't set up when you get it, simply go through the setup screens on the phone and when given the option, choose Restore from iCloud Backup (see image below). If you don't see the backup, set it up as a new iPhone, then go to Settings>General>About>Version. Note the iOS version on the phone. It must be the same or higher version as the one that was running on the phone that was backed up or the backup will not be shown. If that's the case, you need to update the phone in iTune first. Then proceede with the instuctions in the next paragraph.
If the phone is already set up when you you get it, or if you had to update the phone first, then go to Settings>General>Reset, tap Erase All Content and Settings, then go through the setup screens and when given the option, choose Restore from iCloud Backup.
Be sure the phone is connected to wifi and your charger as this will take some time to complete.