Learning how to propagate hydrangeas from cuttings is a simple way to grow new plants from an established hydrangea. Choose a healthy, non-flowering stem and cut a section with several leaf nodes. Remove the lower leaves and place the cutting in a moist, well-draining growing medium. Keep it in a warm location with bright, indirect light and maintain consistent moisture without making the soil soggy. Over time, roots should develop. Once the cutting has established a healthy root system and begins producing new growth, it can be transplanted into a larger container or garden area.