Store-bought potatoes are not recommended for home gardens. They may be sprayed with chemicals or infected with disease that could remain in your soil for a long time.
For best success, purchase seed tubers from a local nursery or agriculture store. Cut them into pieces (minimum 2 ounces or so) with at least one "eye" or bud per piece; prepare them at least a day before planting so that the fresh cut can dry. Plant them cut-side down. (Washing is not necessary; remember, plant them dry.)
While you're waiting for your harvest, eat the grocery store potatoes! Best wishes!