Yes, you will need a separate PSU for the stereo system. The yellow wire of the PSU output is the +12V line and the black wire is the negative.
When an ATX PSU is simply plugged into the mains supply, only a standby power is on. To turn it fully on, the PSU has to be triggered from the motherboard. To do this manually, the green wire on the 20/24 pin ATX connector has to be shorted (connected) with the black wire.
In practice, since the stereo unit draws quite a bit of load current, it will be best to join at least two of the yellow wires together. Same with the black wires.
Also make sure that the PSU's 12V line is rated for 10A or more - preferably 15A. Check the label: it will give ampere ratings for 3.3V, 5V, 12V, etc.
The principles are quite straightforward, but if you don't have experience in electronics, you may have to ask a technician to arrange the connections for you. I've drawn a guide here:
*img43.imageshack.us/img43/3479/psustereo.gif
You may be able to come up with convenient ways to make the connections. For example, instead of cutting the green and black wires from the 20/24-pin ATX connectors, you can take a short length of wire and insert the two ends into the green and black pins.
The load current on the green and black wires is negligible, so you can use this method. But the main 12V lines have to carry a large current, so simply inserting wires into the 4-pin Molex connectors is not good enough for long-term use.