Last year I tested growing potatoes in buckets with the bottoms cut out. Since the bottom is gone, the water drains but you still have the walls of the bucket to contain the "hill" that must be built around the plant. It worked well enough that I decided to try again this year.
To do this I started with some cheap buckets from the home improvement store. I painted them so they would look better in the garden. Then I chose the final location I wanted the buckets to sit in while the potatoes grew. This is the final location because once I begin to fill the inside of the bucket, I cannot move them.
Then I added about eight inches of dirt and compost and placed a seed potato on top. (A seed potato by the way is a potato that has started to grow shoots and has not been treated with a growth inhibitor.) Then I put a few more inches of dirt on top and some mulch. As the plants grow I have added more mulch.
The best part is that harvesting the potatoes requires no digging. I can either lift the bucket up and let them fall out the bottom, or I can tip the bucket over and dump them all out.