To build a potato tower you create a bottomless pot, I have made a cylinder out of chicken wire with no bottom or top.  You then stand it up right and place several potatoes at the bottom on the ground.  You then cover the potatoes with a covering of soil mixed with compost followed by straw.  You then have to wait for the potatoes to sprout.  Once you have a approx 30cm of growth you then surround the plant with soil and mulch and straw, leaving approx 5cm of plant out at the top.  You continue this every couple of weeks until you have reached the top of the chicken wire cylinder. Then you jsut wait until the plants die back, showing the potatoes are ready to harvest.