Is there a piece of hardware you can buy which connects the different zones to different sets of speakers?
see: Audio Amplifier......
Seriously, 'zones' are just different/multiple output channels that are playing independent media streams or be sync'd together.
These zones/channels can have an ip/network component, or they can be direct outputs from a MC machine. Or a combination thereof.
Think of having multiple sound cards in a PC. Each output can be setup as a zone. Or have multiple USB sound dongles.
The output is eventually going to have an analog output that needs to be amplified and fed to speakers (or headphones).
There are also a pile of audio amps/components out there that speak 'dlna' and can be connected to a home network and thusly to a MC 'server'.
In general terms, you want your amplifier as close to your speakers as possible. So in my mind the biggest design consideration is how to lay out the network so that it stretches to each location you want/need those speakers. A close-second consideration is the 'control' of the source material. There are plenty of ways to control the individual zones; anything from running multiple PCs to using simple remote control appliances will do the job nicely.
You're probably going to want a wired network; wireless is (again, generally) too problematic to support serious streaming. YMMV but I suspect that for every person that has a 'successful' home wireless network supporting a lot of audio/video streaming (and everything else they want that network to do) that are dozens or hundreds of people who decide to go wired.
If you want/need to centralize the computer stuff and go with conventional home theater wiring, that's another valid approach.
Don't over think it. Zones are pretty easy.