Updated Video 2017 (for clarity): • How to get the NONE option/remove payment ...
Sorry the mouse pointer isn't there, here's the steps in-case:
1. Open iTunes
2. click on "Account" at the top left
3. "view my account"
4. click "Edit" to the right of Payment Type (Under Apple ID summary)
5. The None option should be visible as shown. IF NOT KEEP READING...
*****If you do NOT have the None option, you may have an unpaid balance or an active subscription - https://support.apple.com/en-us/HT203905
...And if all else fails, contact Apple support
Hope this helps please like if it did and if not, tell me why so I can improve. Thanks!