In this video, Donna Emery, an expert horticulturist who makes videos for the Expertvillage, shows how to properly propagate a hydrangea plant from a cutting.
First, find a large woody stem on the hydrangea that will be the donor for the cutting. The best results will come from using a stem that has not yet started to flower, as the resources of the plant can then be solely devoted towards growing new roots and not be divided into producing both a flower and new roots. Now remove the leaves from the stem, leaving only the top 3 or 4 leaves. These leaves should then be trimmed to ensure they neither touch one another or the plastic covering. Dip the stem up to the remaining leaves in water to help then rooting hormone stick, the dust it with rooting hormone, being sure to shake off any excess. If there is concern of diseases or fungal infections, sprinkle dusting sulfur over the stem. Make a hole in the potting soil with a screw driver or pencil, the place the cutting into the soil up to the base of the remaining leaves. Thoroughly water the cuttings, ensuring the soil is wet all the way through. Now using stakes that are tall and strong enough to prevent the plastic covering from touching the cutting leaves. Cover the cutting with plastic sheeting, and leave it outside in a shaded area to produce roots.
This process is shown and explained in detail in the mentioned video and is well worth the watch.