Step 1 - The Server
You need a computer that you can leave turned on all the time. Unless you're planning to have more than 20 users, you can do fine with that old computer you have collecting dust in your closet. Personally, I chose a computer that was only had an AMD 133mhz processor with 64MB of RAM. This is more than enough power to run both linux and the server software. You don't necessarily need a sound card in this machine if it is only going to be the server. You can download both linux and Shoutcast server for free on the internet. There is also a Win32 version of shoutcast that is very convienient if you want to only use one computer for everything.
Shoutcast is the most widely used software by amateurs out there and well documented, so I would suggest using it. There are other, open and closed source solutions that you can try if you want. I would avoid using any of the Real products as they are resource hogs and more crash prone.
At this point, your server is mostly ready to be used. Obviously, you need some sort of internet access to send your music out to the world, and there are a few things that are optional but make it much easier for you and the listeners.
One thing to consider is your bandwidth. If you are streaming over a 56k modem, you obviously will not be able to send out a high quality stream to a handful of users, while if you have an OC3 connection, you can send out just about whatever quality you want to many users. I personally chose a DSL connection from DirecTV DSL because they offer me a decent speed, a static IP, and allow their users to run servers. A static IP is not necessary but it does make things easier for your listeners. Whether you have a static or dynamic IP, you also would probably want to check out DynDNS to get a free hostname. You can get something like mymusic.dyndns.org or pick from other domain names. They're a great service and have a client to work with dynamic IP addresses too.
At this point, you should have your server set up and configured, and online with your high speed internet access. Now that it's ready, you have to figure out what to do with it.
Step 2 - The DJ
What good would a radio station be without the music? In this section, I will be assuming you installed shoutcast on a different machine than the one you will use to broadcast from. If you are doing both from the same machine, it should be a nearly identical process.
First things first, you have to download and install WinAmp. Chances are, if you listen to MP3s on a Windows based OS, you already have it. Otherwise click on the link above and get it. I personally like it because it uses very little memory and I can hide it as a little bar at the top of my screen so it doesn't get in my way.
Most MP3 players have the ability to install plugins. Winamp has various plugins ranging from graphical output, music editing, and what we are interested in, broadcasting. You can get the Shoutcast DSP plugin, and then look at the guide to setting it up here. Unfortunately, the DSP plugin for Shoutcast sucks. It does it's job in broadcasting the music well enough, but you can't minimize the window it opens without risking crashing Winamp, and the "Disconnect" button doesn't work. I've looked for better DSP tools but have not found one at this point. My workaround is that I drag it to the far left side of the screen and only leave enough visible for me to be able to drag it onto the screen again if necessary.
Step 3 - Let's Talk Together
The next stage is to make your client and server communicate so you can send your music to the server. This is probably more simple when you run both the server and broadcaster on one computer. If you have any firewall software on the server, you will know once you try to access the server from your broadcasting tool. On a typical install of both linux and shoutcast, you will probably want to open up ports 8000 and 8001 in /etc/hosts.allow to ALL. You will probably also want to review the changes you made to your sc_serv.conf file to make sure you can access it. What you put in the "Password:" item in that file should also be in the "Output" tab in the DSP plugin, as well as the hostname or IP of the server. After that's done, you should see it connect when you play a song, and see it start to transfer music to the server. It should say something like, "[1D 1:15:10] Sent 9999999 bytes" in the Status box on the DSP plugin. On the server's console, you should see something like, "<01/05/02@20:30:51> [active] 0 listeners (0 unique)" to know that the server is working as well.
Now that you have your server set up, you are a digital DJ streaming your music, you now need someone to hear it.
Step 4 - The listeners
Here's the easy part. Get your friends to download WinAmp, and give them the URL of your server. Something like http://mymusic.dyndns.org:8000/listen.pls will probably work. Once WinAmp is installed the URL should actually open from a browser, so feel free to put it on your website too.
There are a few things you can do to make the experience a little better for your listeners though, and these customizations are purely for looks rather than function.
In the DSP tool, you can go to the "Output" tab and click on the "Yellowpages" button. You can make the server public so it can appear on the Shoutcast website so all sorts of people can listen to it. I would not recommend this until you have had a little practice and load testing though. However, you can still fill out the Yellow Pages Configuration section. Keep the Description field as short as possible, because it is appended to the end of the song's name. I would leave the URL field blank, because it causes the site to pop up in the listener's Winamp in a tiny window with the purpose of annoying them. The Genre can be very useful when you are being listed on the shoutcast site since they categorize music by that. Also, the AIM, ICQ, and IRC are only useful if you want strangers contacting you. Personally, I would leave those blank. I would also let the Track/Title section automatically update itself with the name of what you are listening to. Another thing that you want to consider changing is on the "Encoder" tab. I like streaming at 64kbps, 22.050kHz, Stereo, but the default is much lower and only in Mono. In moments like these, it is easiest to have another computer to use as a test client. If you do that, remember that there is a delay from what you are streaming to what the user hears.
The server also has a few things you can customize to make things nicer. If you are interested in branding, you may want to make an introfile to list in the "IntroFile:" section of sc_serv.conf. Also, if you think you may not be actually streaming 24/7, you can put something in the "BackupFile:" section to play an MP3 as a backup. There are also advanced logging customizations and other things you can do from here.
Some other tips involve the actual music. It would be a pain to have to sit and select a new MP3 each time you want to stream something, so it's fortunate that Shoutcast lets you stream anything Winamp can handle. I prefer to make a playlist in advance so I don't have to set songs later on. You can also play a music CD and not have to worry about skipping to other tracks too. And, since Winamp has such a diverse range of file types, you can even stream your favorite MIDI or MOD files for your friends to hear. You also probably want to avoid playing anything that is not public domain music, or something that you wrote originally, as people do occasionally get hassled by various record labels and the government for sharing music. The other side of this is that there are hundreds of people broadcasting the latest Britney Spears song, but there are only one or two streaming the greatest Korean Polka hits of all time. By playing something more rare or diverse, you can broaden someone's musical tastes.
Conclusion - You Rock
Now that you have been playing around with a digital radio station for a little while, why not share in the fun? You can allow friends to connect to your server as well and stream the music they might like. Theoretically, you can combine different things onto one channel, and be able to have a whole band playing through one source, even though they are all in different places. The options are as limitless as your imagination, and it's a simple thing to do that requires very little talent. Just like how everyone bragged about having their own personal website 5 years ago, now you can brag about your own personal internet radio station.