The construction of a pebble flower bed involves several steps. Firstly, prepare the ground by removing any debris and leveling the surface. Then, lay a weed barrier to prevent grass and weeds from growing. After that, arrange the pebbles in the desired pattern, using a mix of different sizes for visual appeal. Secure the pebbles with a thin layer of sand to keep them in place. Finally, add a layer of mulch or decorative stones on top to finish the look.