The amplifier works on 12 Volts which may be tapped from inside the computer. A socket is fitted for connecting the speakers, and the input is fed in by a cable to be terminated in a stereo EP jack.
Step 1: Tpa1517 stereo amplifier
The chip, two large electrolytics, and three smaller capacitors will make the amplifier complete. I am adding an output socket too, on board. The input shall be via a stereo cable and there has to be a 12 Volt supply line, as well.
The picture is of the major components arranged on a blank piece of PCB.