Carve the floral foam into spheres ranging in diameter from 4 to 8 inches. As you complete each sphere, place it in a bowl of water to soak.
Trim each green mum so that the stem is 1/4 to 1/2 inch long.
Insert a dowel into each foam sphere, working with one sphere at a time. Match narrower dowels to smaller spheres and thicker dowels to larger spheres. After inserting the dowel, use floral pins to attach mums to the sphere until they cover its whole surface. The result should look like a ball of petals with a dowel sticking out of it.
Stick the ends of the dowels into a vase to arrange the mum balls into an attractive bouquet. If desired, add other flowers to fill in gaps in the arrangement or to create visual variety. Place the vase in the center of a pale green tablecloth and arrange the cloth around the vase in loose folds to create an attractive look.