This technique is useful for limited space in your garden and more intensive than planting in rows. The layout of the garden is done in a grid of 1-foot by 1-foot squares (examples here). That gives us here at the UAF Community Garden 48 squares in our 12′ x 4′ planting boxes.
Other things to consider: space can be further maximized by putting root vegetable next to leafy vegetable as one needs more space underground and the other above ground (you might also want to consider plant compatibility). Furthermore, once a crop matures and gets harvested, another can be planted in its place later in the season. Here is a list of vegetable varieties that do well in Alaska. And maybe you want to consider some flowers as well?!
And finally here is a pdf with more info on organic square-foot-gardening.