This is based on ZC 1.3.7.1 but I assume that 1.3.8 works just along these lines:
Go to Admin --> Modules --> Shipping
then click "Zone Rates" and "Edit"
Set "Enable Zones Method" to "True"
Select your "Calculation Method" (mine is based on weight)
I am skipping Tax Class and Tax Basis as it is not part of your question.
"Sort Order" set to "0" so it comes up first (or as only selection) when the customer checks out.
"Skip Countries" leave blank or enter 2-letter code for places you don't ship to.
"Zone 1 Countries" enter "US"
"Zone 1 Shipping Table" enter the weight and shipping charges such as "3:10.90" whereby 3 stands for (my) shipping weight of max 3 kg and 10.90 is my shipping charge at the rate of $10.90 corresponding to the maximum shipping weight of 3kgs in my case.
"Zone 1 Handling Fee" enter any figure you are charging as a Handling Fee. I don't charge a Handling Fee within Australia so it is set to "0"
"Zone 2 Countries" and "Zone 3 Countries" leave at 00 which would include any country other than the USA.
"Zone 2 Shipping Table" and/or "Zone 3 Shipping Table" enter weight and charges as per "Zone 1".
"Update" and done.
Hope this helps
Frank
https://www.frnt.org/zencart