Fill the spaces within the borders with plants, especially annuals and perennials. For a classic feel, stick to a single plant within each space, as was done here. The topiary-inspired balls that punctuate each bed add some height without distracting from the cool, clean overall look and feel.
Design tip: When choosing plantings, consider their bloom period. A bed of tulips will look charming in the spring, but you'll need something in the space for summer through fall at the very least. Also consider the care requirements; if the bed is fairly wide and tightly packed, it can be difficult to reach the interior plants for deadheading and other maintenance.