Fill a 2- or 3-inch-diameter glass with lukewarm water. You can also use a clean long-necked bottle.
Take a cutting from an existing basil plant in the middle of the season. Get a 6-inch cutting from the end of a shoot. Remove leaves on the lower half of the cutting.
Lower the cutting into the water, letting the leaves rest on the top of the glass or bottle. Set the glass in a sunny window.
Replace the water every other day with clean, lukewarm water. The cutting will produce roots in one to two weeks. You can then move the cutting to a pot filled with peat moss, if you desire, or to a bigger glass.