My wife wants her own Apple account

Apple ID - create a new.      

Apple ID – Create         

Family Sharing.         

Family Sharing - Set up.        

When changing to the new ID, there may be some data loss, but you can minimize it. If syncing photos with iCloud, ensure Optimization is turned off in Settings/Your Name/iCloud/Photos and/or in Photos/Preferences/iCloud. Then make sure full resolution photos are on the device/computer. When signing out of iCloud, if asked whether you want to retain data, choose yes. Messages conversations will be lost if they are addressed to the ID. See the article below for other places that the old ID should be removed. See Winston Churchill's response in the below discussion. Also set up Family Sharing to keep access to your apps/purchases. 

How to switch Apple IDs on your iPhone or iPad.      

How to transfer all files from one iCloud account to another.        

What to do after you change your Apple ID or password - Apple Support.     

Create Your Apple ID - Apple

You may find the following helpful:

Using More than One iDevice on the Same Computer

This applies mainly to couples who are adding another device and do not want their email, messages, etc. being duplicated on both devices. To begin, read: How to use multiple iPhone, iPad, or iPod devices with one computer. You need to establish a separate Apple ID and password for whoever will use the new iDevice. See Apple - My Apple ID and Frequently asked questions about Apple ID. The easiest way is to do this on the computer using iTunes: iTunes- How to set up an Apple ID within iTunes.

On the computer create a new user account for the person with the new iDevice. This will be the user account that person will always use. He/She will no longer use the other user account. This way that person will have a separate iTunes Library. Note that once done you cannot "share" apps under a single Apple ID. Each of you must purchase your own apps under your own Apple ID. When you decide to split up like this one of you will need to re-purchase the apps that they want to use.

Start by transferring the new device(s) to a new account along with all your data. Save any photo stream photos that you want to keep to your camera roll (unless they are already in the camera roll) by opening your Photos app, tap on Albums icon at the bottom. Now, tap on My Photo Stream album; tap Select; tap on the photos you want to select, tap the share icon (box with upward facing arrow) in the lower left corner; then tap Save to Camera Roll.

If you are syncing notes with iCloud that you want to keep then you need to open each of your notes and email them to yourself. Later you can copy and paste the text into new notes created in your new account.

Tap on Settings > iCloud > Delete Account (only deletes it from this device, not from iCloud; the person keeping the current account will not be affected,) provide the password to turn off Find My Phone and choose to Keep on My iDevice when prompted. Sign in with a different Apple ID to create your new account. Choose Merge to upload your data.

Once you are on separate accounts, you can each go to icloud.com and delete the other person's data from your account.

The above was created by the user, randers4. Changes were made to improve readability and syntax.

About Family Sharing

1. Set up Family Sharing
2. Family Sharing - Apple Support
3. Share purchased content with Family Sharing
4. Family Sharing and Apple IDs for kids
5. Share an iCloud storage plan with your family - Apple Support
6. Leave Family Sharing
7. iCloud - Family Sharing - Apple Support
8. Family Sharing and Apple IDs for kids