Pretty, right? Those leaves will hold their sculptural form for MONTHS and all they ask for is a few ice cubes each week. That is it. 3 ice cubes from your leftover sweet tea and your orchid will be happy as a clam. The roots will grow up and out of the pot (see above), but that is completely normal and OK. Orchids in the wild grow on trees with their roots exposed. Don't try to tuck those roots back down into the pot. Just let them be.
You might even move your orchids outdoors for the summer to get a little light, but it is not necessary. Remember they grow ON trees in the jungle, meaning they are under the canopy and do not receive a terribly large amount of direct sunlight.
NOW. Flowers. If you want your orchid to re-bloom, you need to give it a bit more attention. First things first, if you haven't yet, snip off the old stem as low as possible and discard. Then you need this simple recipe: A little more sun, a little more light and a wee bit of fertilizer. Give it a weak fertilizer (a 20-20-20 or a fertilizer marketed for African Violets) and a spot closer to the window or outdoors under indirect sun. Water a few times a week (though do NOT get it soaking wet) and before you know it, that old orchid you were about to throw out will reward you with another show.