You can continue adding as many rounds as you want to your granny square. Each subsequent round will follow the same basic procedures used in the preceding rounds. You'll start with 3 chain stitches substituting for the first double crochet. In the corners, you will work 2 sets of 3 double crochet stitches separated by 2 chain stitches. Otherwise, you will work 3 double crochet stitches in each space, separated by 2 chain stitches on either side.
Learn how to finish the granny square on the next page, and find ideas for using crocheted granny squares: Last page of the crochet granny square tutorial.