Step 1: Getting the Parts
a pair of computer speakers
a pair of nice speakers you wish to upgrade to
spare speaker wire
If you want them to be battery powered, you also need:
an 8 AA battery holder
an extra power supply (it needs to fit in the power input, but doesn't have to be the same voltage)
a 12 volt regulator (or whatever voltage yours are)
Here are some things to look out for when you're buying stuff:
Look for a set that comes with a power supply, unless you know you have a spare power supply at home. For some reason Goodwill has a habit of separating the speakers from the power supplies. I don't know why. But you may need to look through the bin of tangled cords for a power supply with the same voltage as your speakers. Also if you want to power them on batteries, you MUST get speakers that are rated for DC power, preferably ones that run at 9 or 12 volts. You may be able to work with other voltages, like 15, but that might get tricky. They really don't need to be nice speakers. Mine are stock Dell speakers that probably came with a computer. The only control is a volume knob. They cost me $3.
You may need to check Goodwill a couple of times before you find an appropriate pair. Look for speakers with a name brand like Sony or Panasonic. These are usually nicer. You should also check the power rating. A pair of 50 watt speakers usually sound a lot better than a 5 watt pair of speakers, even if you aren't going to power them at anything higher than 5 watts.