Personal File Sharing between Remote Networks

Question

Trying to connect my Mac (OS 10.4.9) in one state to a Mac in another state (OS 10.3.9). I am connected to the internet via Airport. Second Mac is connected to the internet via DSL modem. With file sharing turned on, on both computers, and firewalls turned off (System Preferences: Sharing: Firewall Off), neither computer can connect to either computer via Personal File Sharing (I went to Go: Connect to server... Then entered the correct IP address).
Also, have not been able to use my computer as an FTP server (System Preferences: Sharing: FTP Access On) such that the second computer can connect via Cyberduck (FTP client software).
I know little about all this, but in my research over the last two days I am unsure why my efforts have not worked (for either Personal File Sharing or FTP connections). the following two Support pages on Personal File Shariing have not worked for me:
http://docs.info.apple.com/article.html?artnum=107369
http://docs.info.apple.com/article.html?artnum=106661
iMac G5 2GHz   Mac OS X (10.4.9)  

Answer 1

What is a NAT router? Your suggestion to use a file
storage service as an alternative sounds like it
might be a good idea for me. It's just that the Apple
Support articles made file sharing sound so simple
(i.e. "This allows Macintosh computers in remote
locations to share files with any type of Internet
connection").
This is like saying the Interstate highway system makes it easy to drive from one city to another. It's true, but you need to know something about driving first. Similarly, you need to know something about Internet traffic.
To continue with the highway analogy, let's say your data is like a car. Actually, it's a packet with addressing information inside. The key addresses are source and destination IP addresses. When inside your town, or LAN, it's got local addresses. Maybe your computer is 10.1.1.2 and your printer is 10.1.1.3 and a car destined from your computer to your printer has a source of 10.1.1.2 and a destination of 10.1.1.3. This is like saying take a left at Main Street.
But there are maybe millions of Main Streets. Where this all changes is where we go out to the Interstate, or global Internet. Your router is your gateway to this traffic. It has two interfaces, one side talks to your locality and it has a number like 10.1.1.1, and another side which talks to the global Internet and might have a number like 71.126.45.113. As your car goes through this router, it's source number changes to become that of the router (71.126.45.113). This is so it can find its way back, and others can follow. The local address has no meaning out here. When it (or rather another car) returns, the router swaps the addresses back and sends it to the local network. This process is called NAT (Network Address Translation).
Now, the problem you find is that you can reach the destination router, and what you want is to get to another machine in that locality, but there is no local destination. You get to the toll booth at the end of the Interstate, but the toll taker doesn't know where you want to go. This is where ports come in. Your car has a number which corresponds to a service. In this case, the port is 548 and the services is Apple Filing Protocol over TCP. The toll taker know this. "Oh yes, Mrs. Johnson on First Street handles afpovertcp. Take a left on Main Street." This is called port-forwarding. You set the router to send requests for port 548 to the machine you want shared.
Another possibility would be to disable NAT. This has some drawbacks. If you have more than one machine, you may violate your contract with your ISP. You also open yourself up to certain attacks and need to be much more careful. There's another possibility called DMZ, but that's like disabling NAT for one machine.
I hope this clarifies things. You need to use the addresses of the routers, and forward the ports you wish to use. There's one more consideration: unless you have static IP addresses, those are likely to change. You can use a service like www.dyndns.com to use a host/domain name to connect your machines. It's free and easy.
Powerbook G4, iMac (Intel), and tons of hardware sitting in the closet   Mac OS X (10.4.8)