Hyacinths, hyacinthus orientalis and its hybrids, are in the lily family, planted as bulbs and known for their beautiful, fragrant flowers. The Roman or French hyacinth is native to Southern France and can remain in the ground year after year in areas of little or no winter chill but not Hawaii or other tropical regions.
They do well in cold climates; they are not a tropical plant. Even garden books note that they can be grown in all zones except Hawaii. In areas of the country with distinct cold winters, bulbs can be left in the ground and with proper chilling, will bloom the next year.
For gardeners in tropical regions: as mentioned the bulbs need cold weather to stimulate bloom. Here are some instructions when purchasing a potted hyacinth: after the bloom has died, put the bulb with its leaves in the ground. The leaves should eventually yellow and die back. At this point, dig up the bulb, set it in a small pot with potting soil, cover to keep dark, also keep the soil moist. Place in the refrigerator, it must be below 45 degrees Fahrenheit and remain there for at least 10 weeks. Roots will grow and eventually a shoot tip will emerge. At this point, it can be removed from the refrigerator. This is considerable effort and no guarantee it will work; hyacinths may be one of those plants that has to be purchased each year.