The amplifier connections are what you'd expect: input using twin screened audio cables (shown in blue) and output using heavy-duty speaker cables (black). The DAC connection to the server PC is USB (purple). The Wi-Fi router connections are the usual RJ45 network cables (brown). The monitor connection is also RJ45 with adapters from/to VGA (green) at each end.
Let's ask the remote control for a listing of Michael Jackson albums. The iPad sends the request to the server PC via the Wi-Fi router. The PC reads the information from its internal hard disk and sends it back to the iPad by the same route.
Now that we can see MJ's albums, let's now select the biggest-selling album of all time, "Thriller", then touch "Play Album". The remote control sends this new request to the PC via the router. This time the PC reads the music file for the first track ("The Girl Is Mine") from the NAS drive and sends it in digital form over the USB link to the DAC. The DAC converts the digital signal to analogue and forwards it to the amplifier and speakers. Simultaneously the PC updates the "Now playing" information by changing the monitor screen and sending status information to the iPad display.
The "Sound" panel on the remote control has buttons for adjusting the volume, selecting the sound source, etc. When we press one of those buttons, the command is sent to the amplifier via the WiFi router and the infra-red transmitter, without involving the server PC.
The server PC has no keyboard or mouse, and the only monitor is some distance away in the listening room. When the PC is booted, all the required programs start automatically. For maintenance purposes I control the server PC remotely from another PC using RealVNC.
The diagram above has the things that need to be in sight on the left, and the things that don't need to be seen on the right. Some or all of the things on the right ("equipment cabinet") clearly could be in the listening room: the heat output is modest and they're completely silent except for a slight whirr from the NAS drive. But I've chosen to locate everything I can outside the listening room in a nearby cupboard.