That's an epiphyllum -- you can propagate it by sticking the cut end into a fast draining medium like perlite. I use 'dirty perlite', which is mainly perlite with just a little potting soil, i.e. just enough to make it look dirty. This time of year you shouldn't need any rooting hormone, just keep the cutting humid (not much of a task these days) and the perlite from drying out completely.