Well assuming your site is not on your computer, you'd have to make some sort of connection between the server and your PC.
Usually some kind of SFTP/FTP will do for basic tasks like this. There are many guides on the internet that can help you set this up far better then any advise I can give you.
Yep, if you are on a VPS or dedicated server, rsync is very handy also.
Otherwise a script running on your local computer to connect via SFTP/FTP to your site and download the file will work. You can also do some magic with renaming via the script and keep a weeks worth (or more if you are really creative) locally.