Soap service and sales tax

We are building a new ecommerce site with WP and Woo. Our corporate owners use Vertex for taxation and have allowed us to use a SOAP service to get tax classes and rates. We can see what we need to call, but just not really sure how to make the request in php/woo and have it bring the rates back into the cart page.

Does anyone have an idea on how to accomplish this. We are novice to inexperienced.