It depends
Normally you don't use a central amplifier/distribution system, but have a separate device in each room.
You should also look at the Logitech Squeezebox devices (similar capabilities to Sonos, although Logitech look to be reducing the range of devices available). Basically you don't control the NAS, what you control are the playing devices in each room. Each device then requests the files/audio streams required from the NAS. I'm more familiar with the Squeezebox range, which uses a bit of server software running on the NAS as the mechanism to convert from the audio files on the NAS to the audio streams running over the network.
Devices can either be self contained (network audio streamer + amp + speaker(s)), or just the network audio streamer which connects as a source to an existing HiFi/Audio system. Controllers tend to be iPod touch/iPad or Android phone/tablet devices operating via WiFi. Using the controller you can browse your music library or run a pre-compiled playlist.
For example, I have a NAS upstairs in a spare bedroom, a Squeezebox Touch in the lounge connected to my main HiFi/Surround audio system. I can select what's playing on this either directly on the Touch itself, or via WiFi with an app on my iPod touch. I also have a Squeezebox Radio, which I can use in any room, again I can select the music directly on the radio, or via WiFi with my iPod. I could have other Squeezebox Radios in other rooms, and all could be playing different music from my NAS.