How do US merchants handle their ecommerce taxes when creating orders

Hi all, I have been stuck with a problem for a while and would be happy to pay for someone's time to help me come to grips with the issue.

The background:

I am developing an integration between Sage 300 and ecommerce sales channels like Shopify and Woocommerce.

We sync stock and prices to the sales channels, and then write orders back to Sage 300.

The problem: 

I don't understand US/CA tax system and what a typical setup would look like for a merchant selling online in multiple states, and I can't seem to find this information anywhere.

How do businesses set up the hundreds/thousands of different tax authority/classes/rates for the US, considering that the taxes can be specific down to the city and zip code level.

How do merchants match the taxes on Shopify/Woocommerce to the order's Tax Authority and Tax Classes?

Do they just eyeball the Shopify's tax lines and match it up when creating and Order?

Any help would be much appriciated!