From the backwoodshome website:
"Once the new potato plants get to be about eight inches tall, add another tire and add soil around the plants until just a couple of inches of the tops are above the soil. Repeat this process for the third and subsequent tires. As you add tires and soil to the ‘tater stack, the plant stalk is covered with soil. As you do this, the existing stalk will send off roots as well as grow upward to once again find the sunlight it needs. Since you are gradually raising the soil level eight inches or so at a time, the plant is able to keep growing without suffocating. At the same time, you are creating a 24- to 36-inch tap root off of which many lateral roots will develop. Each of the lateral roots can produce additional potatoes at three or four levels instead of only one. When you water the plant, be sure that the soil is thoroughly moistened all the way down to the base of the pile."
Does that help?
Another interesting method using wire mesh can be found here:
http://www.hillgardens.com/potatoes.htm