How can I change my iCloud account on my iPhone?

My wife had to get a new iPhone and they put my iCloud account on her phone. I am trying to change it but when i go into Settings > iCloud, the email address is grayed out so I can't see how to change it.

How can I change the iCloud account on my wife's phone so she gets her contacts, etc and not mine?

Under Settings / iCloud you'll see a big red button labeled as Delete Account. Contrary to what it appears, it won't actually delete the account, nor your Apple ID, it will only delete the iCloud's content from your device.

So, to change the device's iCloud account just delete the current one and then log in appropriately.