Exhibition growers grow spuds in large polypots but old compost bags can be used also.
Fill the bag with compost or peat and some nutrients (we use Vitax Q4 and seaweed meal), dig a trench and line it with manure, place your bag on this and draw soil around to keep the bag in place. The seed spud is placed near the bottom of the bag. The roots grow through the holes in the bottom (add extra large holes if using old compost bags) in to the muck and soil leaving the potatoes to swell in the compost unhindered and usually free from pest or disease. Water direct into the bag upon planting and then not again until the shoots are well up.
This post on my blog shows what I mean.
Smithyveg!: First spuds in
I think if you put some manure in the bottom of a compost bag and then fill with compost you could even grow them like this on a hard surface such as a patio but then the watering would be entirely down to yourself.