The aloe vera is a succulent plant that is native to South Africa. Like all other succulents, aloe vera stores water in its thick leaves and requires very little water. The plant is typically propagated by offshoots called "pups." Aloe vera plants are also propagated by planting pieces of the original plant to form new plants.
Fill a flower pot with potting mix made for cacti. If you don't have cactus potting mix, make your own my mixing potting mix with gardening sand at a 1 to 1 ratio. Do not pack the mix into the pot. Tamping the soil firmly makes it difficult for the aloe vera to develop.
Use a razor blade or sharp gardening knife to slice off a leaf of an established aloe vera plant. Select one of the large outer leaves; larger pieces develop larger root systems, and will grow faster. Cut a piece that is at least 5 inches long.
Place the cut aloe leaf on a counter and allow it to air out for one week. The cut end must callus (heal over) before it is transplanted. An aloe leaf that is planted before its wound is healed will be vulnerable to disease and rot.
Push the aloe leaf into the center of the flower pot after a week. Bury all but the top 4 inches below the surface of the soil. Do not water the cutting. Treat the aloe cutting as you would another aloe plant. Give it several hours of sunlight per day, but water rarely.