Tillandsias come from humid regions.  They receive their sustenance by absorbing moisture that carries microscopic nutrients from decaying matter.  For this reason, air plants such as Spanish Moss and Xerographicas thrive without the need for a soil medium.  

As with other plants, care factors for Tillandsias vary by geographic region of origin and plant type.  Tillandsias come in two flavors: Mesic and Xeric.  Mesic airplants (tillandsias with smoother leaves) hail from regions with more frequent moisture whereas xeric types (air plants with more white hairs/'trichomes') are accustomed to the arid conditions that they're native to.

Light

Full spectrum bright, filtered light for about 12 hours.  Direct morning light makes for happy air plants.

Tillandsias may be grown indoors or outdoors as long as they receive light.  If an air plant lacks sufficient light, the plant will shut down and will fail to absorb any nutrients from watering (which will consequently result in rot).

Be sure that tillandsias aren't exposed to direct noon/afternoon light as this will scorch the leaves.

When growing indoors, be sure that the air plants are situated no more than 10 feet away from a window/full spectrum light source.

Water

Depending on weather, generally mist once every other morning.  If leaves curl to indicate dryness, an optional thorough wetting for 5-10 minutes once every week or two may be needed.  

Mesic types require thorough saturation every 3-5 days.  Xeric tillandsias may be wet thoroughly every 7-10 days.
Flip Tillandsias upside down after misting/soaking (see Air requirements).  Allow Tillandsias to dry within 4 hours after watering.

Air

Air circulation is necessary for rearing healthy air plants.  Keep a window open around air plants if indoors.

Bearing in mind that Tillandsias receive sustenance from constant moisture powered by air movement, these plants thrive from constant and fresh moving air.  

Mold results from Tillandsias kept wet or have had water sitting within the leaves for too long.

Soil

None needed.

Keeping air plants in soil actually encourages mold growth.  Tillandsias may be mounted on dry, non-porous surfaces.  If mounted on porous surfaces, be sure to remove plant from surface before watering and replace plant on surface after completely drying.