I have wanted to plant potatoes for years. This is the year I am going for it. There are several ways to do this; directly into the ground, in a garbage can, and in a grow bag. For reasons of space limitations the choices best suited would be the garbage can method or the grow bag method.
With the garbage can method you would get a 33 gallon garbage can, preferably the hard plastic type, and drill holes in the bottom and sides for drainage. Then fill with about 8 inches of garden soil and plant a few seed potatoes of your choice (which you can purchase online or at a local nursery). Place can with the lid off in a sunny location. As the plants grow you will add soil to cover the plant, leaving about 4 inches of the top of the plant out of the soil. Do this every week or so until your garbage can has been completely filled with soil. When it is time to harvest your potatoes in the fall your garbage can should be filled with those lovely vegetables. Just dig them out!
The grow bag method (which is what I will be doing) is simply filling the bag half way (which you can purchase online or at a local nursery) with gardening soil, planting about 5 of the seed potatoes of your choice into the soil, and placing the bags in a sunny location. Water as needed and as plants grow add more soil (every week or so), at the end of the season you should have a bevy of beautiful potatoes.