Using advance shipping scenarios is very similar to advanced discounts. The only difference is that you can set what to use in order to determine the shipping fee. The options include quantity, weight, or amount which correlate with the ranges. Read through the description on Advanced Discounts to get an idea on how Advanced Shipping works (advanced shipping profiles can be applied to individual buttons in addition to the built-in cart).
You can apply advanced shipping profiles in up to three different places: across the entire button regardless of custom fields selected, for different price/options selected, and/or for different standard options selected in the button's main standard dropdown field. This is particularly useful if you want to charge a base fee for the button but an additional $1, for example, the XL shirt. Advanced shipping profiles can only be applied to the main dropdown menu under the Customize Fields tab and not the dropdowns from the additional custom fields.