First off you will need to set the app to use either exact postal code matching or partial postal code matching.
Within the app click Settings
Scroll down to the Delivery section and locate the Validation block
Select Exact postal code match or Partial postal code match
How to specify the valid postal codes
Now you must tell the app which postal codes are eligible for delivery. You do this by modifying your Locations delivery settings.
Within the app click Locations
Click on one of your locations' names to reveal the edit page
Locate the field called Eligible postal codes
Enter a comma separated list of your valid postal codes into this field and click Save
Task complete! You customers will now be required to enter one of your eligible zipcodes before proceeding to the checkout process.