You need to locate your product template within your theme — the template where the add to cart button lives.
In many themes it is either in the Templates folder as product.liquid or in the Sections folder as product-template.liquid.
You are looking for the add to cart form within the template.
Look for tag with <form action="/cart/add"...
The snippet {% include 'customer-shipping-rules' %} needs to be between the <form> and </form> tags.
You can also look for your Add To Cart button within the code. You can place the snippet {% include 'customer-shipping-rules' %} right before or right after the add to cart button as well.
If you are having trouble figuring out where to put the snippet. Contact support at info@customershippingrules.com or call (646) 494-2802, we will assist you in adding the snippet in the right place.