From what I understand, the shortlist storymap can only be self-hosted, although I hear they are working on a cloud-hosted version.
You'll need access to a web server to deploy this app. You will put the app files in the same directory. This will probably be done through FTP transfer or in file explorer, depending upon how you connect to your web server. If you need free hosting to test this app out, you could always create a github account and use github pages.
You will provide the app with your the webmap ID. This is what will connect the app to the webmap you author.