Updated December 4th, 2021
Delivery fees can be setup on the checkout page through Shopify settings:
Access your store settings by clicking the "Settings" button on the bottom left corner of the screen and then navigating to the "Shipping and delivery" settings.
Locations available for delivery should appear under the "Local delivery" section of the page from where you can then manage the settings by clicking "Manage".
Different "Zones" can be created based on postal codes or delivery radiuses, and these zones can be configured to show delivery fees.
Once setup, a customer navigating through checkout selects the "Ship" option. Note that the "Ship" options covers both standard shipping and local delivery.
If the customer is eligible for Local delivery, the option will show, along with the appropriate shipping/delivery fees as configured earlier in the "Zones."