Your motherboard will almost certainly have a 3.5mm stereo line out jack, which you'd normally plug the jack from powered computer speakers into. An amp driving the unit speakers does the same job. So the interconnecting cable would be one often described as iPod or MP3 player lead, to go from the 3.5mm on the mainboard to whatever input sockets are on the amp. Those sockets may be a pair of RCA jacks, although some amps have a 3.5mm socket too, also maybe labelled MP3 or iPod.
Car amps now tend to have huge power outputs, which makes many of them unsuitable for your purpose, since they would need far too much current. There's a couple of links below to offer some ideas, they are not specific recommendations, just illustrations, but they may be suitable.
The first looks like a respectable moderate power conventional car amp, that you would hook up to a head unit in the car. A unit like this should be able to be just connected to the computer instead, and if the computer has a powerful enough PSU to give an extra maybe 150-180W, it would likely run from the 12V available in the computer. That would be too much to draw from something like a spare HDD Molex plug though, so a soldered connection would need to be made to the PSU wiring. You mightn't want to go that far.
Another inexpensive possibility to try (with less known about quality) would be little amps available on eBay etc like in second link. They are lower power (ignore the 200W on the example one, it only has 24W power requirement), and could be supplied from a spare HDD Molex connector, or a plugpack. It looks to have a choice of input, both 2 x RCA and 3.5mm stereo.
With each amp, you'd connect the speakers up the same way as car speakers. Clip the wires off the existing connector, and the two speakers would just act as left and right channels. If the speakers have + and - markings, connect those wires to red and black speaker terminals on the amp. If not, you'd just do them both the same way, choose one terminal on each speaker, big or small, for its wire to go to black & the other goes to red,
Edited by Platypus, 10 February 2016 - 06:24 PM.