You already have the secure shell daemon running (which is why putty works) and this includes a secure FTP server. To make this visible to the outside world you need to set up port forwarding on your router so that external connections can be made. On my router for example, this is configured under "Network Address Translation". You need to forward port 22 to the internal IP address of your MyBook (192.168.1.?).
You should then be able to access the FTP server using a secure FTP client. An added complication is that the IP address you show to the world is likely allocated by your ISP and may change every so often. You can find out what it is today by typing "ipconfig /all" in a DOS window, but look into a service such as www.no-ip.com for a solution to this.
If you only want to be able to view files stored then you could consider opening up the webserver already installed on the MyBook to the outside world. This can also be done via port forwarding. This time forward port 80 instead of 22. However in this case you should probably read up on setting up passwords and HTTP authentication and such as it will be visible to the entire world.
Note, exposing ports like this really does encourage unscrupulous ne'erdowells to come snooping so make sure you've got things tied down first. Make sure your root user has a password, or consider disabling root access from sshd. (This forces you to log in with a normal user and password before using su once you're on the machine)