Choose a healthy branch from the mother plant and from the outside of a branch--look for the first "knee" (bumpy mound) beyond where two leaves branch off. Think of it as looking like a Y when you're done, not a V. Pinch the branch off just below the knee.
Fill a small plantpot with the potting soil and give it a good drink. It'll compact down a bit from the water, so give it a bit more soil to fill it to the top of the plantpot. Take a pencil and make an inch deep hole, but elongate it so that the cactus cutting can slide in. Gently tamp the soil around the cactus cutting to make sure the dirt is firmly touching what will eventually be the root. At this stage, I keep the soil slightly damp at all times to encourage root growth.
Offer light fertilizing every month throughout the year, but give it a stronger dose once it has blossomed. Once the plant is established, water lightly once every ten days.Re-pot the plant after the first year into a much larger pot and leave it there for many years. Christmas Cactus love bright shade and even do quite well outside under a tree until it begins to get too cool at night. Give the plant a good hosing off before you bring it inside. Within days it will start budding.