"How do you grow potatoes?"
Jared, first you need "seed potatoes" -- which are either small whole potatoes or cut-up larger potatoes; you can probably find them at a local garden center, or order them from one of the seed companies. (Two varieties that I really like are Red Gold and German Butterball, but there are a LOT of different potato varieties out there.)
Once you have your seed potatoes, spread them out somewhere where they will get light, and they will start to grow some sprouts. You don't want to have them in the dark, because if you do the sprouts will grow really long and weak.
Once you have nice sprouts, and the weather is suitable, you can plant your seed potatoes. Where I am they can usually be planted by early to mid May, sometimes even earlier. If you're planning to grow them in the ground you'll want to dig a trench or holes about 8 inches deep, put your seed potato pieces in the bottom, and then cover them with a couple of inches of dirt (in other words, don't completely fill the hole back in right away). As the plants start to grow, add back more dirt so there is always some of the plant above ground, burying the stem. Something that I learned in just the past few years is that all of the potatoes that your plant will produce will be above the level of the seed potato that you originally planted; so keep adding dirt and pull dirt up to mound around the plants, particularly making sure any potatoes near the surface stay covered so they don't turn green.
When your plants start flowering, you can dig up some of the potatoes to use as "new potatoes," although, some varieties don't seem to actually do much in the way of flowering so then it's more of a guessing game. And when the tops die back your potatoes aren't going to do any more growing and it's time to dig them all up.
After I dig my potatoes I spread them out on some screens made with hardware cloth, in the shade (actually, in my garage), where they will have good air circulation to dry them out somewhat. After a couple of weeks of drying, or more, I brush off the majority of the dirt and store them in paper grocery sacks out in the garage (don't use plastic bags, they hold too much moisture in which causes the potatoes to rot).
They can also be grown in containers of various types, but I don't have any actual experience with that so maybe someone else can advise you if that is what you are interested in doing; at any rate, however you plant them the principle is the same, you start with seed potatoes and gradually cover with dirt (or some other material; straw can also be used, for instance).
I hope this is helpful -- they're really pretty easy to grow!
