Assuming you start with a plant, there are two easy ways to get more plants. These instructions should work for any of the easter, christmas or thanksgiving cactus types.
Cuttings: Twist off a single pad or multiple pads and leave them out for a day or two to dry a little. I put mine in clean plastic containers with about 1/2" of damp potting soil. Push the base of the cuttings into the soil, cover the container to keep in moisture and put under lights, or anywhere with good light that isn't going to cook the containers. I generally do multiple containers so if one goes bad I don't lose all my efforts.
They should start putting out roots quite quickly, after roots they will begin growing out new pads. Once it starts growing new pads it can be removed from the container and put in a pot of its own.
Seeds: Takes a lot longer, but the seedlings are cute... Start with the plant flowering, preferably with several blooms of different ages open. With a paintbrush transfer pollen from different flowers, do this for several days. When the flowers die it will be obvious which ones are now growing seeds, the base will not drop off, and in the case of easter cactus the flower will also stay attached. Months later the fruits will be ready to harvest (mine got lighter in color and sort of squishy to the touch.) I germinated mine with instructions from this link: http://www.therainforestgarden.com/2011/09/germinating-easter-cactus-seeds.html. The seeds will germinate very quickly when fresh, as in less than a week. However they take a while to get larger.
