This website uses WooCommerce, an e-commerce plugin that really simplifies having a shop on your website. It does all the heavy lifting in terms of listing and presenting your products, managing them, and even selling them.
To list a new product is very similar to adding a new page.
Select +New from the top administrator bar, then "product".
A screen will popup asking you to add a new product name. Note that this is what the product is going to be called and organized by WooCommerce.
Set product category under the segment aptly named "Product Category". For this item, the product category is "Book". You can add additional category, which is what the products are organized by.
Set the product image under the segment aptly named "Product Image", which takes you to the media library. Upload a picture or use one that's already in the system. Note that smaller files (the images used for the catalog are 300x380 pixels) are best; larger images slow down the system.
Set item price under the segment aptly named "Product Data - Regular Price". This number shows up as the green dollar amount under the image name when published.
Set item description under the final segment named "Product Short Description". It can be as long as you want, and shows up as the text below the price.
At any time you can view all products under the Products tab of the leftward administrator bar. It shows all your items, the price they are listed for, and more information. From this screen you can also edit existing products, or add or delete products.
EVERYTHING you need to know about WooCommerce is documented on their website here: http://docs.woothemes.com/documentation/plugins/woocommerce/getting-started/