Most succulents can be propagated from leaves and from stem cuttings. The stem of the plant in the photo also has roots sprouting from the stem. Many succulents will propagate from parts of a leaf, and some, such as Kalanchoe “mother of thousands”, small plantlets grow on the margins of the leaves. When they drop off, they root where they land.
Small stem cuttings can be planted in dry sandy soil and leaves can be laid on the surface. Roots will find the soil (geotropism), and eventually little plants will grow at the base of the leaf. Begin to water once they’ve begun rooting, very conservatively at first. And give succulents good sun right from the start, just a few hours of mild sun and then more as they develop more roots.
Haworthia, Aloe, Gasteria, Sedum, Sempervivum, and others, are easy to divide. Remove a clump from its pot, and use a paring knife to separate it into smaller clumps or individual divisions. Pot up into small clay pots, keeping the same soil level. The Haworthia on the right is ready to be divided, but I’ll probably wait until spring.
When working with succulents, do no water immediately after potting up. Any cut surfaces on the roots can rot if they are wet. So, after a day or a few days, they will get their first drink, if the weather is sunny.