The common red orchid cactus is Nopalxochia ackermannii, although the one shown perhaps has a more wide open flower than that species produces. Since more than the one genus (Epiphyllum) and multiple species are involved in the makeup of the many different cultivars of orchid cacti, the alternative term Epicactus has been coined.
Easy to propagate from cuttings - cut off a shoot, allow it to dry off a few days to form a callus on the base (to stop decay getting in), and plant in a pot. Growing conditions: grow in composted bark / leaf mould mix. Water when the mix gets dry. Normal indoor temperatures are OK, don't let it get below about 10° in winter or above 30° in summer.