Google "ShoutCast server" turns up official docs, downloads, and forums.
It does not look awful.
I have done "live broadcast" with RealMedia's tools (I do NOT think you want to do RealMedia!). The concept seems similar. There is a public server which clients access. On a different machine you run a bit of Producer software. Tell it where your mic and camera are, it crunches them to a data-stream. Tell it some kind of "key" which authenticates you to the public server as a known uploader. Your program needs a name, and there may be other fields you can fill. Press Start and you are on the air.
As in some other fields, publicity (getting the word out) is harder than technicalities.
I probably spent a couple days setting up my own Real public server (with Shout you use their public servers), another day in arcane corners of the producer software; Shout's really better be a lot easier. I think I ended up with three PCs counting a client; Shout handles the one in the middle and with today's PCs you can probably produce and client on the same machine (risking feedback in speaker-mic).
You need an uplink path which is faster than your program datarate. I would not try video or good audio from here: the wire to Maine is long and congested, plus RR sharply caps my uplink speed to a fraction of anybody's downlink speed. For this and other reasons I would put shows in a can for non-real-time viewing.
And the basics. Mike close to mouth. Well padded room. GOOD light. Probably simple background; don't make the compression eat patterned wallpaper, it takes bandwidth away from important objects. Tele-prompter or ad-lib your choice, but do some full rehearsals to break-in the rough edges of your delivery and gain skill with camera and producer-ware.