1. Click on Settings button on your iOS device:

2. Click on Passwords & Accounts. In older versions of iOS, the option is called Accounts & Passwords:

3. Click on the account that you will delete:

4. Click on Delete Account.

5. You will be asked again if you wish to delete the account. Click Delete Account again.

6. The account is now deleted. You can close out of Settings.

Note: If the "Delete Account" button is not appearing, you may need to turn off all locations in which the account is being used by deselecting them.