You can propagate aloe vera plants by seed or by replanting the baby offset shoots that grow around the base of the mother plant. Seed propagation is tricky, but removing and replanting the offsets is simple. The offset shoots emerge from the aloe plant's roots, and then grow their own set of roots to become a new plant. Offsets tend to grow profusely around the mother aloe vera plant when the parent plant becomes root bound in its pot, is under-watered or is otherwise neglected.
Remove the offsets from around the base of the aloe plant when the shoots are at least 4 to 5 inches tall. Gently dig up the offset plants with their roots using your fingers or a spoon.
Set the offsets on a flat, dry surface in a well-ventilated area for two or three days. Wait to replant the offsets until their roots dry and form calluses.
Prepare a 6-inch planter pot with drainage holes in the bottom for each of your new baby aloe plants. Add to the bottom of the planter pot with about 1 inch of pea gravel and fill the pot with a mixture of equal parts potting soil and peat moss, or you can use a cactus potting mix.
Make a small depression into the potting soil using your finger or a spoon that will accommodate the offset's roots. Set the roots into the soil depression and gently pack the soil around the roots.
Water the potting soil evenly to moisten it. Cut a Styrofoam cup in half and place the top half of the cup over the baby aloe offset to help it stand up.