Summarize:

Seed potatoes are crops that grow root sprouts. These sprouts poke out of the spud and grow shoots. Seed potatoes can grow several of these sprouts per potato. Use small to medium-sized seed potatoes for best results.  You can select seed potatoes in a variety of types, such as Yukon, Ida Rose, and French Fingerling, for example. Make sure to use seed potatoes, not potato seeds. Potato seeds will produce plants with different characteristics than the parent plant so you may not get the desired results. A kitchen table near a window works well, but you can use any sunny space with a flat surface. Leave your potatoes in the sun until you see sturdy, green shoots. Your potatoes will grow healthy and quickly if they are kept in moderate lighting at about 60–70 °F (16–21 °C). If you want to slow down the growth of your potatoes, place them in a colder spot away from the sun. Your seed potatoes are ready to go in the dirt when they grow about 1 in (2.5 cm) tall. You will see the shoots growing upwards from the potato sprouts. If you want to grow more potatoes, use a whole seed potato with at least 4-5 sprouts. If you want to grow large-sized potatoes, cut your seed potatoes into chunks with at least 1-2 sprouts on each. Each potato will have a different number of sprouts.  Full seed potatoes will grow smaller potatoes, though you will have a greater potato yield. Chunks of seed potatoes will grow large potatoes, but you will have a smaller yield.
Purchase at least 4 seed potatoes from a nursery early in the year. Put your egg cartons on a flat surface in a warm area for 2-3 weeks. Plant your potatoes when the sprouts are 1⁄2–1 in (1.3–2.5 cm) long.