Donna, I have the white one, but I imagine the care is similar. It's very much a tropical baby, wanting humidity, warmth (nights never below about 55deg.) and bright shade. After they bloom it's good to give a little dry, cool rest period, then begin watering and fertilizing again to prod it into new growth and bloom.
Since mine is out in my garden, it gets Florida weather - cool and nice in the winter, and hot and muggy all summer. It blooms off and on all summer, from about April until we get our first cold front in the winter. (this year it was mid-Nov).
I give it a sprinkle of time release pelleted fertilizer in March, another around the end of May, and other than that just keep it moist when the weather's warm.
Here's the Database entry, lots of good info and pictures here:
Flamingo Flower (Anthurium andraeanum)