package dimensions are only used for over sized items, for smaller items, you should the item weight.
if you want to use the dimensions, you would add columns to the cart object for length, width and height,
then in the add to cart button, set those values.
then edit the Shipping rate lookup server behavior on the confirm page to bind the package dimensions to the cart columns.
the shipping in eCart is just a rate lookup, as the seller, you have to set up the shipping labels and set up the pickup by UPS. you would pay for the shipping at the time the package is shipped. if you prefer via a different method, you can certainly that up.