Strawberries can be planted using one of two planting methods: the matted row, or the hill system.
In a matted row, plants are placed in a row about 18 inches apart, with rows placed at least 3 feet apart. As the plants grow, they produce runners freely and form new little plants. You can steer the runners so they grow towards adjoining plants and fill in the empty spaces to make a row matted with strawberry plants.
In the matted row system, plants are treated as biennials, so, for an ongoing bed, you need to make a new planting each spring, which is harvested the summer of the following year and then tilled under. If you keep the bed for an additional year, so many new plants develop that the bed becomes overcrowded and the plants produce a small crop.
In the hill system, plants are set 12-15 inches apart in a bed consisting of three rows, each of which are also placed 12-15 inches apart. Plants are treated as perennials, with all runners cut off as soon as they form. By not letting any new plants grow, the plant puts all of its energy into current plants, producing large plants and berries.
The hill system takes more plants initially, and requires more attention from the gardener, but the system also saves the work and cost of annual replanting. In a hill system, strawberry plants will continue to produce for six or more years.
You can use either method with any type of strawberry, but June bearing plants are most often planted using the matted row system. Everbearing and day neutral strawberry plants are often planted using the hill system, as less runners are put out by these varieties.
If you need a definition of June bearing, everbearing, and day neutral strawberries, check out the article.