You would either upload by using DirectAdmins file manager (as archive would be easiest with this option and then extract on the server), or by connecting through FTP, the server address would be your hostname, the username for the service (randomized on creation of service, seen as ******* @ x##) and the password you set when creating the service would be your login credentials)
To get the site on your own domain you would need to make sure files are uploaded to the public_html folder that relates to that domain, each domain would have their own set of folders including public_html.