I am going to do a basic rundown of the basics of networking.

How does an IP address work?
When you connect to a network and you open your browser you have the same external IP address as another computer on your network.
What happens when you connect to your network is you connect to the router and the router connects to the internet. Your computer never gets close to the internet.
When you are on the network you have your default gateway ip which allows computers on a network to communicate to each other. While you connect the routers do the same thing.

for example on your network your computers ip is "192.168.0.10" but the ip of your router is "11.11.11.15".
its like handing your friend a letter to give to your friend.

What is a port?

A port is a open section your computer uses to interact with the internet. A port has to have a service to open it, if it doesn't have a service it isn't open.

while we talk about ports it is a good thing to mention 3 types of services. Applications, Servers, Protocols.
A application is what you use to connect to the internet (like mozilla or internet explorrer.) a server is what you connect to. A protocol is a list of rules for the tcp/ip to run by.

A few things are all 3, FTP and telnet are the first to pop up in my mind.

Setting up your router.

With networking comes the router. The router is what LETS you connect to the internet.
To LOG in to the internet you need to type your default gateway into the urlbox in the browser.
(to find the default gateway go to start | run | type cmd | type ipconfig and hit enter.)
once you type it in you will get a popup box. Normally the password is admin, admin, but sometimes it is: superuser, password.
Once you are on there is a password section. This is where you add a password to your router. Add a "wep" password. Once you are done click on save.

There should be a admin panel or logs panel, this is where you can view the ips on the network and MAC addresses.
You can see the ip of the websites that are visited on the network and more.

If someone is on your network you don't want on it go to "mac filter" or "filtering" and you can add the mac address of the computer on here. This will ban them from the router which wont let them online.
This is also the section you can block websites from being entered. If you have a child you want to protect you can add some words on there to block.

I hope this helps,
S_R_SA guy might wanna add that a router is only necessary when more than one computer is sharing a local area network. (One exception is using a router as a "firewall" to help shield your computer from nefarious "crackers" on the Internet.) The router acts as "traffic cop" / postal worker to route data packets between the various computers sharing the network and the network access POINT (be it cable modem, DSL modem, T1 line. (Me? I want at least OC768 [oc = optical carrier] or the equivalent of 768 megabits per second capacity, but that probably won't happen for a long time!)