Turn on FTP and Remote Login in the Sharing pane in System Preferences. This will allow you to connect to your mac via ftp, ssh, or sftp. You might want to create an extra user account just for file storage and transfer if you want to restrict access to certain directories.
You'll be able to connect to your mac using a good ftp/sftp client. I recommend
Fugu. Your address will look like this:
<username>@<ip address>
If you know your way around the terminal, the following commands will work:
sftp <username>@<ip address>
Connect to your mac.
get <filename>
Download a file.
put <filename>
Upload a file.
If you want to connect to your new file server outside your home network, you'll have to set up
port forwarding on your router, which should be explained in your router's manual. You'll want to forward all traffic from port 22.