You can propagate Delosperma echinatum by division, cuttings, or seeds. Cuttings can be taken in fall, spring, or summer. Although, for plant division, spring is the ideal season.
First, start by taking a stem cutting of 2-3 rows of pickles. Second, take off the bottom row of pickles. Third, once the ends have calloused over, plant the stem into soil or water. Additionally, the pickle leaves you take off can be planted straight into the soil as well.
Pro tip: Dip the ends of the cutting (or single leaves) in a rooting hormone to promote the development of roots.
Finally, wait about 2 weeks, and then finely mist the soil daily. Although, the soil should never be super wet. Once the plant starts producing roots, you can switch to regular watering measures.