First, forget about planting in rows (if you ever did). With this method, planting areas are one square foot. Each square foot can be planted with several, equally-spaced plants: for example, one broccoli or tomato plant, four lettuce or Swiss chard plants, nine bush bean or beet plants, or sixteen carrot, radish or onion plants. Transplants or seeds are spaced the recommended distance on each side, but no rows are left in between. This means no thinning and less seeds wasted, and since they grow close together, the ground is shaded, preventing weeds and holding in moisture.
The next main thing is that the beds are not dug. This is different than in most intensive gardening methods, where the soil is dug deeply and a lot of amendments are added, at least in the first year. This method recommends building a six-inch tall raised bed filled with what is essentially a home made potting soil mix: 1/3 peat moss, 1/3 vermiculite, and 1/3 compost. Each time a square is harvested, more compost is added before it is replanted. This mix is fertile, holds moisture, and grows few weeds, while making harvesting easy. I am not convinced that the closely-spaced plants need only six inches of soil to grow in, but apparently this works even when there is a bottom on the bed. Eventually, however, the plant roots would probably break down the soil under the garden and improve it, even without digging.
I like the tone of the book, which aims to deliver the most productive garden for the absolute least investment of time and money. In fact, the Square Foot Gardening Foundation is a non-profit organization that has humanitarian projects around the world. For more details on building a Square Foot Garden, check out the "How to" section on the website, which has most of the necessary information on it.