As already mentioned the core part of the interface is the 4066 IC. Each 4066 IC has 14 pins, four control pins, 4 pairs of switching pins , and 2 pins for power supply. Each control pin can turn one of the switch pairs on or off. Pin 14 is for the positive powersupply and pin 7 for ground.
As you can see the control pins are pin 5, 6, 12, 13. These pins work at "the logic level" that just means that they are either high or low, high meaning at +5 V, and low meaning +0 V. In other words if you apply +5 V to pin 13 then pin 1 and pin 2 will be shorted together, and the same goes for the rest of the control pins.
Now this is very practical, because the data pins of a computers parallel port work at exactly the same logic levels, +5 V for high, and +0 V for low. That means that you can connect the data pins from the parallel port directly to the control pins of the 4066 IC. As luck is the high / low status of the parallel ports data pins can fairly easily be controlled from software. The parallel port has 8 data pins so two 4066 IC's can be controlled.