You can propagate a yucca plant by taking cuttings from the plant or from offsets at the base of the trunk.
From cuttings
Take a cutting: In spring or early summer, use clean, sharp shears to cut a 3-inch or longer piece from a mature part of the plant.
Prepare the cutting: Remove all but the top few leaves to reduce moisture loss.
Dry out the cutting: Place the cutting in a cool, shady spot for a few days to allow it to dry out.
Plant the cutting: Put the cutting in a pot with potting mix or a cacti and succulent mix. You can also add rooting hormone powder to the base of the cutting.
Water and place in a warm spot: Water well and place the pot in a warm, sunny spot with indirect light.
Wait for roots: After a few weeks, new roots should form and you can repot the cutting.
From offsets
Cut an offset: When repotting the plant in spring, use a sharp knife to cut off an offset from the base of the trunk.
Dry out the offset: Allow the wound to dry out for a few days.
Plant the offset: Put the offset in a new pot with potting mix and water well.
Place in a warm spot: Keep the pot in a warm spot.
You can also propagate yuccas from seed.