Hydrangeas respond well to several propagation techniques, including layering and dividing. But Dirr's method for rooting softwood cuttings in summer will yield a bunch of new plants in about four weeks.
To do it, locate a stem of softwood between the hard, woody growth at the bottom of the plant and the fleshy green tip by bending it; softwood should snap cleanly. Cut a softwood shoot that has several leaves. Trim it into 5-inch-long pieces that each have a leaf toward the top. Remove extra leaves; Dirr goes a step further and cuts the remaining leaf in half to minimize evaporation (and the need for watering). Dip the other end in powdered rooting hormone; plant the cuttings in trays filled with a soilless mix and perlite. Cover with a plastic bag, and stash in a shady location, misting regularly to keep the leaf hydrated. After four weeks, tug on it to check for roots; once roots are developed, transplant to a bigger pot and feed with a slow-release fertilizer. By next spring, cuttings will be ready to go in the ground.