I've planted not only more, but also a larger variety of potatoes this year than I ever have before. Here is how I do it (a pretty common approach, but sometimes photos help).
Some people cut their potatoes into small pieces with at least two eyes before planting. This year, I chose to leave my potatoes whole. Though I haven't done this before, Pat Welsh, in Southern California Gardening, suggests that they may be more productive this way.
I leave the potatoes out in a warm, bright place so that they can begin to grow. This is called chitting. Developed sprouts, already putting out roots, help the plants grow more quickly as soon as they hit they soil.
Because some varieties, though from my experience not all, produce more potatoes the more they are layered with soil, I grow potatoes in deep, 15 gallon pots. Here is a line of pots along the very edge of our ranchito.
Potatoes grow best in loose, slightly acidic soil. This year, I mixed regular potting soil with leaves and coffee grounds; I added about 6 inches of this soil mixture to each pot, then gently wiggled two potatoes into the soil mixture until they were completely covered with soil.
The potatoes are already growing well. Once the sprouts are about 4 inches tall, I'll add another layer of the soil mixture to the pot. As they continue to grow through the early spring, I will add soil with every 4 inches of growth. This will allow the potatoes that are below the soil to be well-protected, and it will allow the varieties that sprout more potatoes from covered leaf notes to be as productive as possible. Several times through the growing season, I will fertilize with fish emulsion or liquid seaweed.
This year's varieties include Viking Red, Purple Viking, Purple Peruvian, Ozette, and German Butterball.