With the release of ACP 2, there is a sudden proliferation of web-controllable telescopes. Some of these are deployed on a home network hooked to the internet through a dial-up, cable modem, or DSL modem. Here's how to get your telescope web server visible from the other side of these devices.
Connection sharing is possible through a technology called Network Address Translation (NAT).
Every machine on a network must have a unique IP address, and these are either assigned on an as-needed basis by your ISP (using DHCP) or else you are assigned a static IP address which never changes. (Sometimes DHCP-assigned IP addresses can have very long lifetimes, but they still aren't static.) If you have several devices on the local side of your cable or DSL modem, then they all need unique IP addresses, or the network wouldn't work. Unfortunately ISP's are usually not in a position to give additional addresses out, because of the limited supply of IP addresses available for their services.
The solution is to assign a device - either a dedicated routing computer or a black box router of the sort provided by Linksys, Netgear, etc - to interface with your ISP's network. This device tells your ISP that it is the only machine on your network. At the same time, it assigns addresses to all the machines on your local network using DHCP. These addresses will be in the 192.168.x.x address space. This range of addresses is nonroutable so the traffic can't leak out to the rest of the internet.
In 'normal' IP networking, different services use different "ports" - for example, web services use port 80, and e-mail uses port 110. There are lots of unused ports available. So your router assigns a port number to each of your machines' nonroutable addresses. Any traffic coming into the router on port x is automatically forwarded to the corresponding machine.
This is called NAT, and it is why you can share an internet connection.
(Note: NAT can be cracked, so you still need to run a firewall, or run the risks of not running a firewall.)
Although NAT can be cracked, you shouldn't try to hack through your own NAT router every time you want to load a page from your scope control server. There is a more elegant solution. What is needed is a way to put your telescope control computer into a stable namespace. If you run your own DNS server you shouldn't be reading this. If you don't, then there are several services that will help you out. These work by defining a namespace for your server, and keeping the entry updated for changes in your router's IP address. These solutions are mostly referred to as DDNS, or Dynamic DNS.
At this point it is best to just go have a look at these services yourself: