Here's what to do to be successful with Amaryllis (For you technical people, the real name is Hippeastrum, but most people only know it by the name Amaryllis, so we will call these beauties by that name):
If you have a bare bulb to start with, pot up the bulb in a pot a little bigger in diameter than the bulb (clay is preferred to add "ballast" to keep the plant from falling over). Bury about 1/2 - 2/3 of the bulb, leaving the rest above the soil line. Keep in a warm location (but not hot) and keep soil moist. Once the bulb sprouts (the blooms stalks will emerge first), keep in a sunny location.
As the bloom shoots emerge try to not have the plant in too dark or too warm of a location. That will make for tall, spindly bloom stalks that cannot support the huge flowers.
If your blooms stalk does fall over (you could help prevent this with staking if needed), it can be used as a cut flower, lasting a week in water.
As the new growth (blooms and then foliage) appears, keep the soil moist but not wet.
All spring and summer we treat amaryllis like any other plant - keeping it actively growing. Do not cut off the foliage once the blooms are spent! You need to keep the plant growing its foliage all summer into the fall. They need part to full sun, and should spend the summer growing outside in its pot (from May, on).
Though the foliage needs to remain all summer, the spent bloom stalks should be cut off near the neck of the bulb.
After growing all summer in its happy place, it will need to come inside by October 1st (or earlier if there is frost). Starting around October 1st, do not water the plant! Slowly the leaves will dry up. By mid-November cut off all leaves - dead, dying, and green - close to the neck of the bulb. Keep the bulb in its pot.
Don't water your bulb until new shoots appear - about 4-10 weeks after cutting off the foliage. As the new shoots emerge (these are bloom stalks) start watering it again and keep it moist but not soggy. The dry period gives it the rest it needs to get ready for its next big show.
Amaryllis like to be pot-bound so don't plant in too big of a pot. You can re-pot in a couple of years if you feel the need to.