Here is all you have to do. Ready?
STEP 1. You will need a tall container (at least 30" or so), like an old trash can or half whiskey barrel . Drill some large drain holes in the bottom. The trash can is the easiest because if yours are like mine they already have some holes in the bottom from dragging them out to the street. Be sure to scrub them out well and then do a rinse with 1 part bleach to 5 parts water. This will kill any bad stuff lurking in the corners.
STEP 2. Next, fill in the bottom with several inches of loose planting mix. Use a mix that has a good amount of peat moss in it. The acid level helps prevents potato scab.
STEP 3. Plant the potato or several potatoes a few inches deep into the container. It's best to use Seed potatoes that you can buy in January or early spring at your garden center. If you can't find them or you have your own potatoes that have sprouted that's OK but not as good a yield and might have disease problems. For the heaviest yield plant seed pieces about the size of a small chicken egg. Use certified, disease-free seed potatoes when possible.
Soon your potatoes will grow!
STEP 4. When they have about 6 to 8 inches of foliage add some more soil mix covering about ½ to 2/3rds of the stems and foliage. Do this every time you have a flush of new growth. Soon the potato plant will be flowering.. Every time you add a layer of soil add some good organic fertilizer. You want those potatoes to grow vigorously until they start to flower. Then stop feeding.
STEP 5. Be sure you keep your potato barrel watered but not so much that it gets soggy. When the potato plant is blooming well you can check them. Dig down into the barrel and feel the potatoes growing on the roots. The potatoes at that time will be small. We call them new potatoes. They can gently pull some of those new potatoes up for an immediate treat. Yummy boiled in their skins with butter or maybe cut up, sprinkled with olive oil, salt & pepper and cooked in the oven. MMMmmmmm.
STEP 6. After the plants are done flowering and begin to turn yellow then the potatoes are reaching their full size (poke around to see). Stop watering and let the tops die back. Let potatoes cure in the soil for a few weeks, then dig them out by hand or tip the container to harvest. Your whole family will love eating their own potatoes and be ready to try it again.
Pick up some organic potato starters here...
There are other places to get potatos, sure, but you're guaranteed non-GMO seeds from Seed Savers. Below is a photo of potatoes growing in a store bought container (especially for potatoes), but save your money and use a trash can or barrel.