Unless you have the Advanced Shopify plan, you won’t be able to make manual price adjustments based on international region. Shopify automatically calculates the price of your products for international customers based on the customer’s shipping address, but if you plan on frequently receiving international payments you can set pricing regions and adjustments if you go to the Payment section in Shopify’s Settings.
Shipping is available on all of Shopify’s plans and actually has partnerships with several logistic providers like DHL and UPS to help provide it. Simply list your shipping area (eg: North America) and print out a shipping label using the Shopify app. You will need to have accurate package details for location and weight, plus provide your own packaging material.