When to Plant: In our part of Texas, potatoes should be planted between the last part of February and the first week of March. The old rule of thumb is George Washington's birthday, Feb. 22. Tops of plants are sensitive to frost, and planting earlier may result in a crop failure due to freeze. Planting later often results in seeds rotting or low yields.
Seed Prep: Irish potato plants are actually grown from tubers, the underground piece of modified stem which stores starch, which we call a "potato". About 2-3 weeks prior to planting, purchase your "seed potatoes" and place them in a slightly warm, dark place to stimulate "eye" formation. Once the eyes are well formed and about 5-6 days before planting, cut each potato into chunks, each with an eye. Chunks should be roughly the size of a chicken egg. Place the cut pieces in a well-ventilated area to heal over to help prevent rotting and disease. Pieces can also be dusted with fungicide or sulfur to help ward off disease.
Planting: In a well prepared garden row, place potato pieces 10-12" apart. Cover with about 3" of soil, firmly but not packed. If planted too deep, potato pieces may rot before they reach the surface, or soil temperature may be too cold to allow for growth in a timely manner. An initial application of fertilizer down each side of each row is recommended, but do not allow fertilizer to contact the seed pieces. Additionally, try to rotate planting location so that plants of the potato family (potato, tomato, pepper, okra) are not planted in the same section of the garden more than once in 3 years. Disease can build up in the soil quickly if crops are not rotated.
Care and fertilization: As plants grow, pulling soil or mulch up around the plant tops will help give more room for potatoes to form underground. When tops reach 6-8", use a garden hoe to "hill up" the soil around the stems of the tops, leaving a few inches of top showing. Most potato plants benefit from a side dressing of fertilizer when the tops are about 4" tall, about 1 cup of an all purpose fertilizer per 30 feet of row, depending on your soil. Potato plants need regular, even watering for best growth and quality of potatoes. Irregular watering can result in misshapen and oddly skinned potatoes; too much water can lead to rots and disease problems.
Harvest: Most potato varieties are ready for harvest in about 100 days from planting. In our area, this will be the end May. You can tell a plant is ready for digging when the tops begin to yellow and die. Also, you can gently dig by hand for a few potatoes at a time throughout the growing season, as long as you take care not to disturb the plant or root system too much. When harvesting the whole crop, use a shovel or garden fork to dig well under the potatoes, then lift up and let soil fall away. For best results, dig while soil is slightly moist, not overly wet or dry.
Storage: For optimal storage time, gently dust the soil off and let the freshly dug potatoes dry. Then store in a cool place with good air circulation.
Fall potatoes: Seeds used for fall potatoes are usually the small (1-2") potatoes saved from the spring planting. Fall potatoes should not be cut, but otherwise are prepared in the same way. In our area, mid-August is the recommended fall planting date, with harvest in November depending on frost. Excessive late summer heat contributes to rot, disease, and insects, so be on watch and treat at the first sign of a problem.
There are several alternative ways to grow potatoes, such as in a barrel, or in tires stacked on top of each other as the tops grow. These methods often work well and simply capitalize on the ability of the potato to produce more as soil is brought up to the growing stems.
For more information on growing potatoes as well as how to identify and treat common pests, check out this Aggie Horticulture page: http://aggie-horticulture.tamu.edu/vegetable/files/2010/10/E-511_irish_potato.pdf
Interesting history of the Irish potato and other fun facts: http://www.plantanswers.com/garden_column/020902/020902.htm