Growing potatoes in a trashcan is fun and easy. In case you think, "Potatoes are cheap, why do all this work?" price heirloom varieties at Whole Paycheck sometime.
A lot of communities have gone to high tech trashcans that can be emptied by an automated garbage truck. This leaves the householder with old trashcans, which can be used for low tech urban potato farming.
The first step is to locate a sunny spot. Potatoes are not really choosy, but they do like sun and water. If your sunny spot is over a patch of dirt, cut the bottom off the trashcan with a Sawzall or a hacksaw. If your sunny spot is over concrete, drill drainage holes in the bottom of the trashcan. If the trashcan is really disgusting, clean it up a bit.
Next, put your trashcan on your chosen spot and fill it with four inches of cheap potting soil with a handful of bone meal mixed in. Head off to choose your potatoes. You need about a quarter pound organic potatoes per trashcan. Look for potatoes with nice big prominent eyes. If you have potatoes that have started growing in your pantry, use those.
Cut up the potatoes so you have one or two eyes per piece. Many people leave the potatoes out overnight to skin over, but I have never bothered. Put the pieces about six inches apart on top of the dirt in the trashcan, then cover with another couple of inches of potting soil and another handful of bonemeal. Don't bother to tamp down. Water so that the dirt is as wet as a wrung out sponge. Cover the trashcan with a piece of chicken wire or an old screen to keep critters out.
Keep the dirt moist, and in 2-3 weeks you should see sprouts. Potatoes grow along the stems, so when the sprouts are 8 or nine inches tall and have nice glossy leaves, shake some more dirt along the stems. The plants will grow towards the light, so keep covering the stems as they grow. Keep them watered and the potato plants will grow for about three months. Eventually they will die down. Stop watering. When the plants are deceased, knock over the garbage can and pick out your potatoes.
Note: Reposted from dkos. For those who learn more easily from seeing than reading: