You can verify if your server port is open with a test service such as Shields Up! or Can you see me. (Note: If you are setting up a Web Server, your ISP may block port 80, and so it won't work. If it doesn't show open on the Shields Up! test, double-check your settings. If necessary, you can change the port your web server users. Click here.)
The way you connect to that server depends on which of the Mac's servers you are running. For example:
Select Connect to Server from Finder's Go menu.

Unlike when you are at home on your own LAN, the server won't show up on the list of servers. Enter the string "afp://" in the "Address:" box, followed by the External/Public IP Address of your home network, e.g. afp://66.167.43.161

After a painful delay, you should be prompted for a user name and password. Enter a short user name that exists on your home server's Mac, and give that account's password. After another delay, the server's Public folder should mount on your desktop.
Congratulations!
The Mac Finder offers read-only FTP access to FTP sites, including your own. Select Connect to Server from Finder's Go menu.

Enter the string "ftp://" in the "Address:" box, followed by the External/Public IP Address of your home network, e.g. ftp://66.167.43.161

After a delay, you should be prompted for a user name and password. Enter a short user name that exists on your home server's Mac, and give that account's password. After another delay, the server's volume should mount on your desktop.
Most browsers, including Safari and Internet Explorer, offer read-only FTP access to FTP sites, including your own. This applies to Windows users as well as, so it's an easy way to share files with them, too, using a tool you know they have. Users can either browser the file system (by accessing a directory) or download a specific file.
Enter the URL "ftp://" in the address bar (instead of the usual http://) followed by the External/Public IP Address of your home network, e.g. ftp://66.167.43.161

After a delay, you should be prompted for a user name and password. Enter a short user name that exists on your home server's Mac, and give that user's password. (Just leave the "Account" field blank.) The account name you enter determines the Home folder that will be accessed.

The account name you select determines the home directory that is used when determining the directory or file accessed. E.g. When I specify "http://66.167.43.161/Public/filetodownload.doc" and log in as user "car1son", IE downloads the file filetodownload.doc from folder /Users/car1son/Public/

You can use this to eMail people links to files you want them to download, too. Most eMail programs will let them just click on that link and download the file. (Note that they could, if they wished, use the same usename, password and URL to access any other files you have under that account, so don't put files you don't want them to see in an account you give them the password to, and don't use your own account for the password to send them!

This will actually access the web page index.html in the Sites folder of user "car1son".
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THE END