Ok Methtical here is what your going to want to do.....
you get your cuttings, if the cutting was taken from the middle of the mother cacti, you need to figure out which end is up(in the air) and witch end is down(goes in the soil).
if you are ordering from a supplier, your cutting will come ready to plant, it does NOT matter if it has roots or not, it will root on its own...
plain ol' "CACTUS MIX SOIL" works great to get your cutting going, then after a few months you can move it into some fancier soil.
take a say 5in diameter and 6in deep pot, and put a small rock over the hole in the bottom of the pot(this is to keep the soil from running out the bottom of the pot when you water) i like clay terracotta pots, the cactus rootlets seem to like to grab onto the clay pots sides more than plastic, but plastic works just fine...
take your "fresh out of the bag DRY cactus mix soil" and fill your pot with 3in of DRY soil, this will leave you with 3in of space left in your pot, take your cutting and put it bottom side down in the middle of the pot, fill in the remaining space with DRY soil up to the top of the pot, your cutting should be buried deep enough so that it doesn't topple over, 3-4in should be plenty deep, adjust depth if necessary...
Bam!!! your done....easy as 3.14159....
this is the first stage in your new cacti life, it will grow roots over the next few weeks/months, this is a very slow process it will do it on its own. resist the urge to dig up your now comfortable friend to see if roots are forming.
put your now potted cacti somewhere (not freezing, cold is fine) like on a window sill, where it gets at least a couple hours of direct light a day for now, when the weather gets warmer move it out doors for optimal growth, or to a window where it will constantly be bathed in NATURAL light.
VERY IMPORTANT!!!!! DO NOT WATER THE SOIL DURING THIS STAGE UNLESS IT IS VERY HOT DRY SUMMER WEATHER!!! your cutting has all the water it needs stored in its self to stay alive for months on its own.
Methtical, this is especially important for you since it is winter(quite cold and wet weather) where you live, if you water during this first stage, your cutting WILL ROT because it doesn't have roots to soak up the moisture yet...
after a few months (or when warmer dry spring/summer weather comes) of being in the dry soil roots will have started to form, now your cutting is stable and can be watered without fear of rotting, cacti(especially cuttings) do not require hardly any water during the winter. during the summer when it is hot and soil drys quickly i water once a week(this is for established cacti) and they suck it up readily....
good luck all who are called to grow these beings, it is a very worthwhile (life long) relationship. and remember it is going to take FOR EVER(years)for your cacti to get to a point where you can harvest them, and when they do finally get to this stage its hard to actually cut them down....
Sometimes the lights all shining on me, other times I can barely see....