I remember helping my father years ago do this. He did the one where you slowly fill the barrel with straw so that after the barrel is filled to the top you have a ton of tater's with virtually no cleaning necessary.

It takes a lot of water (remember we are supposed to have a drought this summer) to grow container potatoes.

The trashcan needs to be kept somewhat cool otherwise the tubers towards the edges tend to rot (remember we are supposed to have record breaking heat this summer). Potatoes need full sun to do well.

This technique does work but it isn't necessarily easier than regular garden soil growing - maybe for some people in certain areas but not for everyone.

Another way to accomplish this is to raise them in used car/truck tires. You start with the first tire and as the plant grows you stack more and more tires on top and fill with straw or mulch or soil. By the end of the year you undo to the whole stack and harvest. Easier than getting a lot of light down into the bottom of a trashcan.