Clone aloe vera plants in two ways: either from offset shoots or from seeds produced by the plant. Propagating aloe vera plants from seed is rather difficult, because you'll need two different clone species that bloom simultaneously in order to cross-pollinate to produce seeds.
To clone your aloe vera plant easily and successfully, you're better off harvesting the offsets and replanting them to create a new plant.
Prepare a 6-inch planter pot with a drainage hole in the bottom for the baby offset. Fill the planter pot with a mixture of one part garden soil or all-purpose potting soil and one part peat moss.
Look for baby aloe vera plants, or offset shoots, growing near the base of the adult plant. Gently pull one of the baby plants out of the soil by its base, using your fingertips to lift up as much of the offset shoot's roots as you can.
Make a small depression into the prepared potting mix. Place the roots of the offset shoot into the potting mix and cover the roots with the soil, gently firming down the dirt around the base of the plant.
Water the baby plant to moisten the soil down to the roots. Keep the soil moist by watering the offset once or twice every week, but ensure that the water is draining well and not compacting the potting soil.
Place the baby aloe vera plant in bright, indirect sunlight and keep it around 70 to 80 degrees Fahrenheit. Repot your aloe vera plant to a wider container when the roots spread enough that they become too wide for the pot.