Yeah there's a good way to do that and a bad way to do that.
Difference being the amount of blood involved.
Take the plant out of its pot so you can get at the offsets from the side and the bottom, away from the spines. Remove all the top dressing and maybe use the point of a chopstick to carve out the soil right around the base of the offset, so it has more freedom of motion. Remove the offset by using a sideways wiggling motion. I like to go from one offset to the next and wiggle each one a little, then get back to the first and it will move more. You'll get a much better sense when you've done it a few times. The key is a sideways motion.
Ideally you want to retain as much root as the offsets may already have developed. That's something to pay attention to once you've released the main connection with the mother, maybe use a chopstick to work in and around the roots so there's a way they can slide out. If the offset has no roots, then pot it up anyway and it will sprout new ones. Just protect rootless offsets from direct sun and try to be patient.
To be clear, there are two ways these plants branch: at the base, axillary branches, which is what I'm talking about; or at the growth point, by division into 2 or 3. Both types of branching are evident in the second picture above. The second kind of branch is rather difficult to separate and start (different approach required) but it's sometimes all you've got to work with, given an older plant.
It is a great banner, and I do appreciate you sharing your expertise.
Try some dyckias, Tim! They're all fun.
