In your control center you should have a part where you can configure access. Among these options, there is FTP and also SSH. Configure SSH access, and log in. If you come via Windows, you have to have a SSH client. Putty is pretty much standard.
In your shell session, you've logged in to your home directory. Your move command is almost right, but you should use a path relative to your home (leave the initial slash away) and use forward slashes
/ instead of backslashes
\. If you want to automatically generate a directory name with a date, you have to look into the basics of shell programming.
Experiment with this:
mkdir "`date`" (that are quotes and backticks) and
mv -r path/to/fromfolder path/to/tofolder
EDIT: Commenters are right, it should be noted that the
date command between the backticks gets executed. Anything between the backticks will be executed and if it produces output, it will land there.
And (of course), you should familiarize with the commands you use, for that (depending on how the host is configured) try:
info date and/or
apropos date (and so on)