Set up your shipping rates and taxes in Shopify first. Then when you create the order through the API, Shopify applies those rates and tax rules to calculate the totals. The accepted answer points to the tax and shipping-rate manuals for the setup, then the order create call carries the computed amounts.

Context: Stack Overflow question (score 21): an app takes payment with Stripe and creates orders in Shopify, but needs correct tax and shipping amounts for the order.