Good potato crops start with good seed potatoes. You can get certified seed potatoes that are free of disease at your local garden store, as it's dangerous to use old potatoes because they could be carrying disease. You want your soil to be silt, sandy loam, high in organic materials and well drained. You can use compost or leaf mold to enhance the organic materials, but never use fresh manure. If the soil is poorly drained, the potatoes will rot before they even sprout. Be sure that the soil pH is not higher than 6.5. If it is higher than this, you could end up with potato scab. You also want to avoid using lime, which raises the pH of the soil.
Plant the small seed potatoes whole. For the bigger ones, cut them into two or three smaller blocks. Try to leave two or three eyes, or buds, on each piece. Cut them a couple of days before planting and leave them in a warm place to dry out and heal. Use sulfur to douse the potatoes after cutting them up. This will protect them naturally from rot. Ten pounds of potatoes can be treated with about 2 ounces. The sulfer also works to lower the pH of the soil.
Try to plant your potatoes five to six weeks before the last frost. If it frosts again before the shoots pop up, it should not be a problem; however, if they have already sprouted, try to protect them from the frost. After the last frost, plant your main crop of potatoes.