Well, for basics, what you need are the following for a 24/7 radio station.
1: A dedicated PC that is running 24/7 or a server with a large supply of good quality music (128kbps minimum, higher is better).
2: A streaming server. This can be hosted either at home (if you have a fiber optic connection with 20Mbps+ of UNTHROTTLED, UNCAPPED upstream connectivity) or at a datacenter. If at a datacenter, a server with a plentiful supply of Bandwidth. If hosting from a datacenter, you need a connection that has a greater amount of upload than the stream's bitrate, as well as a connection that is both unthrottled and uncapped. Saturating your upload to the limit will choke your connection, and cause the stream to cut in and out when you're online. Also, capping is self explanatory, and throttling will cause the stream to skip.
3: Software such as ShoutCAST to perform streaming, as well as some slight knowledge of networking and some knowledge on PCs.
4: Of course, if playing music that is retail, you need permission as it is normally copyrighted. Typically the artists of the songs will allow you to play them as they want you to help get their music out to the world, but the music labels, it all depends on what they would like, since they tend to be a bit more picky about streaming/piracy than the artists since they get most of the money anyways.
But that's all that's too it. Might I also include, you need a good ear as well so that you can hear the sound quality and determine what might need to be changed, so some sound knowledge is also needed a little bit.