In order for Shopify to query Webshipper for shipping rates, you need to make sure that you have the feature "Third-party calculated shipping rates" as part of your Shopify subscription plan.
This is included by default in an "Advanced Shopify" subscription, however you can also contact them and have it enabled for a smaller plan either for an added cost of $20 per month or for free if you are paying for your subscription on an annual basis.
Once you have the feature enabled for your Shopify account, you need to create a shipping zone that makes use of the Webshipper Rate Provider as the carrier.
This way, Shopify will query Webshipper and receive the list of carriers that you have configured in your Webshipper account.
To get started, log in your Shopify account and click on "Settings" and select "Shipping."
Now click on "Add shipping zone".
Enter a name for the shipping zone, select which countries it should cover and then click on "Add rate" under "Calculated rates", and click on "Done".
Select "Webshipper Rate Provider" as the carrier, make sure that "Automatically offer new shipping services when they become available" is enabled and click on "Done".
Finally, click on "Save".