The easiest way to propagate Sulcorebutias is from cuttings. Most of them produce a lot of offsets. All those offsets can be use as cuttings.
Take off carefully the offset from the main stem and let it dry for about a week. Afterward I set out the cuttings on clay grains and I spray them frequently (I try to do so in the morning and in the evening). When the roots start appearing, I repot the cuttings in the usual soil.
Sometimes it is even easier : some of the offsets are already rooted. In this case, I just let them dry for 2 or 3 days and afterward they can be repotted in the usual soil.
All those operations cannot be done in the full sun. When the cutting shows some sign of growth, then it can be gradually exposed in the full sun.
How to save an old cutting ?
If you still have some dehydrated, unrooted cuttings from previous year, you can always try to soak them in water. Sometimes, if you are lucky, it works : after only 2 or 3 days a root might appear.
You can repot the rooted cutting in the usual substrate and soak it.
Afterward, the soil must be kept wet but not soaked.
After 5 or 6 weeks the cutting should be perfectly rooted !