Zen Cart is not something you add onto your site. It *is* your site.

You don't use anything like Site Studio to edit it; products and categories are added in the ZC admin panel, and the content of some pages is edited in admin > Tools > Developers Toolkit.

Other things are done by editing PHP files and the stylesheet in a file/text editor like Notepad++ and uploading to your site with an FTP program like Filezilla.

There is a template override system that lets you create a custom template {starting from one of the existing ones) and switch between templates. Look at (sorry, site offline) for a selection of free templates available. Any of these can be downloaded and installed, and then modified by you.

Read the FAQs for an overview of how things are done.