Fill a planting container with half sand and half commercial potting soil, or a commercial potting mixture formulated for cactus. Any container will work, but a 1-gallon coffee can with drainage holes poked in the bottom will ensure that the new agave won't require re-potting for at least a year.
Use a sharp, clean knife to cut an offshoot, or "pup," from the base of a larger, healthy agave. Include the stem that attaches the pup from the parent plant, otherwise there will be nothing to develop a new root. You may be able to remove the offshoot by hand, but wear gloves because most agave leaves have very sharp tips.
Cut off any damaged roots with scissors or garden shears and leave about one-quarter inch of roots on the pup. Dip the base of the offshoot in rooting hormone and plant it in the potting mixture.
Put the new agave outdoors in filtered sunlight or keep it indoors in bright, but indirect light. When you notice new growth, move the agave into full sunlight.
Keep the potting mixture slightly damp. Remember that rot is the enemy of all succulents. Don't allow the soil to be soggy and never let the bottom of the planting container sit in water.
Feed the agave an all-purpose, water-soluble fertilizer in April and again in July. Apply the fertilizer according to the directions on the package.