Potatoes take two to four months to grow, according to About.com. At the earliest stage of maturity, the spuds are referred to as "new potatoes."
New potatoes can be harvested when the plant is about one foot tall. Fully grown potatoes are best harvested toward the end of the growing period when the plant tops are dying and when the location is not in danger of frost. The National Gardening Association recommends allowing the potatoes to dry or cure up to two weeks in an area that is 55 to 60 degrees Fahrenheit. The potatoes then can be stored for several months in an area that is 35 to 40 degrees Fahrenheit.