It is pretty simple to set up actually - pretty low tech from a user's perspective and easy to set up once the initial purchases have been made.
There are also a few ways to do this. I'm not an Apple Fanboy but have found that the following Apple-based system is reliable, as long as your WiFi signal is strong enough. Other than your computer, the following two pieces of hardware are all that is needed:
1. An Airport Extreme, used as a wireless router. This is what will stream the music from your computer to other parts of your house. I have previously used non-Apple routers (e.g. Belkin) with varying levels of success. But Apple talking to Apple tends to be much easier to set up and save you hours of fruitless head-scratching and Googling.
2. An Airport Express, used to receive the audio signal streamed from your machine / router. This little unit just plugs into a power point, and has a headphone jack on the bottom. This unit receives the audio sent from your computer (via the wireless router e.g. Airport Extreme), and using the headphones jack you can just plug the output into the stereo / speakers of your choice.
Out of the box you'll be able to set up iTunes to stream audio from your computer to your remote speakers i.e. whatever speakers you have which are plugged into the headphones jack of the Airport Express.
iTunes will do the work to make sure the audio stays in synch, so if you walk away from your computer playing music into another room which is remotely streaming the music, it will all be in synch. Nice.
With these couple of bits of hardware, you will be streaming music from iTunes. If you want to go one step further, you can stream ANY audio from your computer to your remote speakers. e.g. stream online radio, YouTube, system sounds, you name it. This is great if iTunes is not the only program you wish to be tied to when listening to music or audio. To stream any audio, get the brilliant AirFoil from Rogue Amoeba.
Once set up, you can then ready my other tips on optimising the quality of your WiFi signal. More iTunes related audio tips can be found in the iTunes section of my blog.
Hope that helps! Happy listening.