Expanding a bit on Charles's correct but brief answer...
Suppose your website is on www.example.com and stored in /var/www. At home you have a computer with a directory called /backup into which you want to write copies of the remote files. You can run:
That will create the directory /backup/www with copies of all the files and directories there. You'll need to have root privileges on the remote machine. The best method for setting that up is using public-key authentication in SSH so you don't need passwords. One other option to avoid passwords is running rsync in daemon mode on the server. Read the rsync man page ("man rsync" at the prompt) for details.
sudo rsync -av www.example.com:/var/www .
Eventually when you have your backup configured to your liking, you would put the commands into a script and run it from cron.