Peltier units are designed to operate at a voltage between 3-12 volts, and the 5 volts from your USB port work just fine. Although the amperage could ideally be higher, the 500 mw output is acceptable. Cut away the end of an old USB cable (or pick up a cheapy) and strip back a couple of inches of the plastic covering. Inside you will find 4 wires, usually within a braided or thin aluminum shield. The wire colors will be white, green, red, and black. Trim back the white and green wires, strip off a small bit of the black and red wires, and solder them to the red and black wires of the peltier unit. Wrap with electrical tape or use heatshrink tubing. If you need information on correct soldering procedure or the use of heatshrink tubing, there are many excellent Instructables that will gve you all the information you need, simply do a search!
Optionally, you can attach a 1K limiting resister in between the red and black wires, although you are quite safe at the voltage and mA to not really need one.
Now, plug in your USB cable to a USB port on your PC, and within about 30 seconds you will be able to feel one heatsink become very cool while the other becomes warm. Note which heatsink becomes cool, as that's what we'll want to encase inside the mini fridge.