A Christmas cactus does have a more formal name. It is “Schlumbergera” although it is sometimes called “Zygocactus”.
First of all, your Christmas Cactus would love to be in indirect light. It does benefit from some good sunshine but it doesn’t belong on a window sill that gets sun all day long. It will love your usual room temperature of between 65-78 degrees. It is important to keep it away from drafts and heating vents. Too much sunlight can burn the leaves. You can tell your Christmas Cactus from other varieties because they have scalloped stem segments. Easter and Thanksgiving Cacti have pointy teeth along those stem segments, and of course, bloom closer to their holidays.
As with so many other plants, it likes a humid environment. Either have it standing on a pebble filed tray with water that will evaporate up and around your plant. I have to tell you, I have never had to do this with my Christmas Cactus, but I could be more pleased with it’s power to bloom. Maybe that has something to do with it? At any rate, it does like to be misted on occasion, and be kept evenly moist. Don’t let it dry out completely. It does need to be watered often enough not to let the soil dry out completely.
I understand putting the plant into the bathroom in the fall will help you get a profuse amount of bloom come Christmas. They need some solid darkness to set those blooms. If you have friends with these plants in marvelous bloom, ask them what they do to encourage that. They may not have a clue what their secret is, or they may have some very good tips. Gardeners usually LOVE to share, all you need to do is ASK!
After it has bloomed you should do a bit of pruning. Look at the plant and trim back any extra long “branches”. Also, remember to remove the spent blossoms. This pruning will encourage more growth making your plant look fuller.