Note: all prices in USD
Easiest, cheapest way is to just get an FM transmitter and hook that up to the audio out on the PC. You then tune into the station on the stereo and you're all set. This only costs about $10-15.
You could also get wireless speakers, but I assume you probably already have a system that you are happy with. If not, wireless speakers work on the same principal, but cost significantly more. You'd probably be looking at $50+ (depending on the quality of speakers you want.
There are WiFi access points designed for just this use. Basically, it's a mini computer with wireless internet with a couple of stereo outs. You connect to it over the local network and program it to play whatever from the computer. It's all very simple, but expensive. I think you'd be looking at $180+ for this solution, though it is the best one for ease of use and quality.
You could also set up a dedicated PC to and some fileshares. A dedicated PC solution could be as cheap as $150 if you look (pricewatch.com) and do not need to control the track list from it. On the other hand, you can make a pimpin solution by adding the input (keyboard, mouse) and monitor, for possibly a $300-350 solution.
XBox has an expansion that allows it to act pretty much as a Media Center PC, for like $80. With the cost of an XBox being $150, this one's a pretty good solution as well, at $230 plus the use of a television. You'll also have an XBox. Even if you already have an XBox, you can now play system link games, which is pretty cool.
You could also work up a custom solution for about $100 if you are an electronics/embedded programming guru.
I would probably suggest finding one of those WiFi access points designed to do exactly what it is you want to do. Other than that, the PC and XBox solutions are probably the most cost/effort effective if you consider that they are both added value solutions. The FM transmitter, though, is great for its ease of implementation and cost, though depending on your stereo system, there might be a slight loss of fidelity.