To setup your Facebook store, you need to create Facebook page first. You can easily create page using your existing Facebook account. In the page you will get option to setup Facebook store. Facebook store is not a dedicated website but a tab in your created Facebook page.
Creating Facebook store
It requires some technical knowledge to create a store. For example listing product and allowing user to buy. You can do it by using Facebook app.
There are several websites offer the Facebook app service. Shopify, Bigcommerce, Wix to list a few.
You can attract only Facebook audience through the store. Hope there will some plug-in or extensions which help you share the contents of Facebook to Google+ and Twitter.