Summarize:

The amaryllis should lose its foliage as the summer ends and autumn begins. When this begins to happen, start giving the plant slightly smaller quantities of water, but do not allow the soil to dry out completely. Trim the yellow or brown leaves once they have withered by cutting them off next to the neck of the bulb. Allow living green leaves to remain on the plant. Once the weather is cooler and most of the leaves have died, bring the amaryllis indoors. Place the pot in a cool, dark area between 40 and 50ºF (5–10ºC), such as a basement. If you do not have a suitable area for a pot, you may carefully remove the bulb and roots from the soil and place it in the crisper (vegetable drawer) of a refrigerator.  Always bring the amaryllis in before the first frost, which typically occurs at 32ºF or 0ºC night temperature. If storing in your refrigerator, do not store fruit in your refrigerator at the same time. Many fruits, especially apples, release chemicals that can sterilize your amaryllis bulb. Leave the amaryllis in the cool, dark environment for at least six weeks. Do not water it during this time, but do remove any remaining leaves as they die. This is the bulb's dormant period, and the plant must experience this in order to bloom again. If you want the amaryllis to rebloom by a particular date, such as Christmas, remove the bulb from the cool area at least six weeks before that day.
Reduce watering gradually as the leaves die. Remove the dead leaves. Bring the plant to a cool indoor area. Leave the bulb alone for 6–8 weeks. Move on to the next section after 6–8 weeks.