If your host as set up zencart for you, and you can now see both the CATALOG side (where customers will go) as well as the ADMIN side (where you administer the webshop), then you will do all admin on the remote server.
Remember... this is NOT a flat "html" website.
It is a DYNAMIC website, where the web pages are "cobbled" together from a variety of resources - the most important being the database.
Each page is rendered according to what your shoppers have asked to see.
The product information (the name, product model, price, description, etc) is all called out of the database.
If you are completely new to dynamic-content websites that call data out of a database, then apply the results to a template, you would do well to undertake some online tutorials about this.
But for now, order the book (see top right of this screen) and get familiar with all the features in the ADMIN side of your new shop.