First you need Commerce Shipping, and either Flat Rate and/or UPS installed.
Under Store > Configuration > Shipping, You'll see Shipping Methods and Shipping Services, each of which has configurable rules.
Let's say you've got 2 types of shipping – $15 flat rate within the US and UPS Air to Europe.
In a Shipping Service you might call "flat rate USA", click "Configure component".
Under "Conditions", you'll add a condition Commerce Order / Order address component comparison.
Data selector is commerce_order, Address is shipping address, Address component is country, value is equals US.
The key things to figure out are how to use Rules (events/conditions/actions), and to use the "Order address component comparision."