How much water do they need? Bromeliads that have a rosette of overlapping leaves that retain water (often called "tank bromeliads") should have the rosette kept full of water. Distilled water or rainwater is generally better than tap water (especially if you have hard water). It is a good idea to empty or flush the tank every couple of months and refill it with fresh water. This will clear out organic debris and lessen any chance of fungal rot. In nature, these plants have evolved to catch organic matter, which rots, fertilizing the plants. In cultivation, growers like to keep their plants tidy and debris-free and supplement them with fertilizer to make up for the nutritional loss. Keep the soil around the bromeliad moist (but not wet). This is especially important for non-tank bromeliads as they draw their moisture primarily from their roots. For "air plants" like Tillandsias which are grown attached to a piece of wood, cork or sometimes nothing at all, they should be misted a couple of times a week and even more frequently during the dry winter season when grown indoors. As an alternative to misting, plants grown indoors may be dunked or soaked in water for a few minutes to rehydrate the plant. Make sure to drain away any excess water caught between the leaves as this may promote rot.
How do I fertilize them? Bromeliads are generally slow growing plants that do not need a large amount of fertilizer. The best method seems to be use slow, time-release fertilizers lightly sprinkled around the base of the plant. Never place fertilizer grains directly in the cup of tank bromeliads, doing this will probably burn the foliage and might foster the growth of algae or invite rot. Liquid fertilizer is another good method (especially for air plants that cannot be fertilized any other way). Use 1/2 to 1/4 of the recommended strength and spray several times per season. Flush tank bromeliads occasionally to prevent the buildup of salts that may damage leaves.
Some bromeliads (particularly the grass-like Pitcairnias) can be "pushed" to grow quicker by adding extra fertilizer. Most, though, will not benefit by excessive fertilizer which will tend to make the plants "leggy" (excessively long leaves) or, in the case of those with colorful foliage (like Neoregelias), it will diminish the colors turning the plant green.
Bonus points if you can name the new Genus [It was Tillandsia.]