To start a potato cage, you really need 6X6 concrete wire.  This makes the best cages.  You can also use regular wire fencing with the large openings, but I like the concrete wire best because if you want to harvest some new potatoes, you can reach through the openings in the wire without having to remove the entire cage.

I find it best to kill the grass in the area you place the cage about 2 weeks prior to placing the cage.  I use vinegar for this purpose.  Most people can't get 10% vinegar, but you can use 5% vinegar just do not dilute it.  Use it straight in a sprayer.

After killing the grass out you can either till the soil or not.  I usually do not till the soil though some people prefer to do so.  Just spread several layers of newspaper and about 4 to 6 inches of compost or straw over the area, place the cage and then put either small seed potatoes or cut pieces of potatoes directly on top of the compost or straw. Space the potatoes as far apart as you would in a straight row in your garden, but instead of just in a straight line, space them equally in every direction.  I normally space them 8 to 10 inches apart.  Cover this with about 6 inches of straw wet down and wait for the potatoes to grow through the straw. 

After the potato plants are about 6 inches over the first layer of straw, cover them up with another layer of straw.  Wet this straw down and be sure to keep the straw moist at all times.  This is to be repeated every time the plants get 6 inches over the top layer of straw.  Some times you can get the plants to grow all the way to the top of the wire cage.  I have had luck doing this here in south Texas.  When the plants start blooming, do not cover them with anymore straw.  Let them bloom and die back.  Also cut back on the watering at this stage.  When the vines have died, you can remove the wire cage and harvest the potatoes.  You will find you grow more potatoes in a smaller area this way.  Also the potatoes will be clean and will not be cut or damaged with digging tools.