To share a remote screen using Back to My Mac, or to do screen sharing via iChat, the Screen Sharing program, or VNC, you may need to make changes to the way in which your router controls access to your local network from the rest of the Internet.
In the ideal case, your gateway is directly connected to a broadband modem (or perhaps even integrated in the same box with it) and your ISP has a simple topology—network architecture. When you configure the gateway in this situation, you directly affect its remote accessibility over the public Internet.
In the worst case, your ISP has multiple layers of network address translation (NAT)—a way of sharing an Internet connection among multiple computers—that makes incoming access nearly impossible, and thus remote access for screen sharing inaccessible.
Note
Bypass this section if you have all public IP addresses!You can avoid all the complexity in this appendix if all the computers you want to reach remotely have public IP addresses—that is, if each computer has an IP address that can be reached directly over the Internet, as opposed to a private IP address that is assigned by a router to each local computer. If your network's IP addresses start with 10, 172, or 192, it's unlikely that they're public; you usually have to pay more to an ISP to have public IP addresses assigned, too.
You need to set up your router differently depending which technique you are using to do screen sharing:
Back to My Mac and iChat can use special features in routers that allow automatic port assignment. With those features, a remote computer's whereabouts can be registered in such a way that other computers can find that computer, even if that computer is behind a network gateway that otherwise obfuscates its location. I explain how to handle this case below.
For a direct connection, follow the instructions ahead in Use Manual Port Mapping, which allows you to connect a specific port and private IP address for a given computer with a public port and IP address on the router that can be reached remotely.