Remove the pit covering from the avocado. This is a little difficult to do, but if you slip the tip of a paring knife under the thin side just right, it makes it a little easier. Use toothpicks to suspend the avocado pit, flat side down, over a glass. Add water until the base of the pit is immersed. Keep it in a warm, dimly lit spot. The pit will crack eventually, and a root will emerge, followed by a stem shooting upward.
To encourage branching, cut the stem halfway down when it's from 7 to 8 inches high, cutting directly above the spot where a tiny leaf is forming. The stem will branch at this spot. Put the plant in bright sunlight. As branches grow, periodically pinch off the growing tips to promote fullness.
Avocado plants can be started and grown in soil or water. Keep the soil evenly moist. Leaves will brown if the soil dries out.