When you visit a website, your Web browser knows to connect to the website on a predefined port number. These port numbers were established by the Internet Assigned Numbers Authority (IANA). The standard port used to connect to websites is port 80. Port 80 must also be "open" on your network if you wish to run a Web server on your own computer, so that other people's browsers may connect to you.
Contact your Internet Service Provider to determine if they allow you to run a Web server on your home computer. Consumer-level Internet services are typically provided for general home or home office use. As such, providers do not allow the average consumer to run a server on his home computer. Assuming this is allowed, you can proceed to Step 2. Some Internet Service Providers (ISPs) may block port 80 via settings on their equipment, in which case no matter what changes you make to your home network, you will not be able to run a server.
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Consult your router documentation for information on either "port forwarding" or "virtual server" setup. The idea here is that, although your Internet router blocks all ports by default, you want to "redirect" any requests coming in on port 80 to the computer that is actually running the Web server. If the computer on which you want to host your server is using its own firewall, you will need to consult its documentation to learn how to create an exception for port 80.
Visit a website that will let you test your port forwarding results, such as Can You See Me or Shields Up (see Resources). Make sure your Web server is running when you perform these tests. Another sure-fire way to check if port 80 is unblocked is to have a friend in a remote location (across town, for example) attempt to connect to it using your public IP address or domain name.
Do not expect stellar performance from a server run on a home Internet connection, but if allowed, the service should be able to handle two or three connections at a time.