Hello MaVen, and welcome.
You can root your Christmas cactus
for using water: put put about 1 cm of water into a wide mouthed glass (example is a short plastic cocktail glass) it should root.
As for in dirt:
First let the fresh cutting to dry at least a few hours to avoid potential stem rot from excessive moisture.
Use a moist peat and sand soil mix . Insert the segment about a quarter of it's length into the soil...avoid placing the pot in direst sunlight. Water sparingly the first 2 or 3 weeks to avoid rotting. You could try misting it well. after 2-3 weeks it should show signs of growth at the tips of it's leaves, which is usually reddish in color. after the cutting has rooted you can transplant the cutting into a pot of loose potting soil, and to add a little sand and or compost would be good.
good luck !