I don't have permission to upload files to the root of my shared hosting space
This is not an accident, the initial directory you access using FTP (for Ecohost servers) or SFTP (for Webarchitects and Ecodissident servers), your home directory, often represented as
~/ is set not to be writable by you.
You will however find a
~/private directory where you can upload files that won't be accessible via the web and you will find the
DocumentRoot for your web site under
~/web/ for Ecohost servers,
~/public_html for Ecodissident servers and
~/sites/default for Webarchitects servers — this is where you should upload files that you want to be accessed via the web.