Definitely a tillandsia, Ionantha maybe. Indirect bright light and a soaking in lukewarm water every few weeks, as well as occasional misting, should keep it thriving. Like sympodial orchids, each growth blooms only once and then declines. It continues to provide energy to the pups it will produce soon after the flowers are gone, and when the pups reach a third of the mother's size they can be separated if you wish.
Mistking
Looking for a misting system? Look no further. Automated misting systems from MistKing are used by multitude of plant enthusiasts and are perfect for Orchids. Systems feature run dry pumps, ZipDrip valve, adjustable black nozzles, per second control! Automatically mist one growing shelf or a greenhouse full of Orchids.
I agree with seamonkey that it is a Tillandsia, not an orchid. I purchased a Tillandsia hybrid Stricta cluster while in Florida in April and it looks very similar to yours. It was in flower when I purchased, flowers died off and it's now creating babies, it has pretty much doubled in size. I hang it in my arbour with my orchids and mist a couple of times a day (when I can). A neat little plant.
That's a Tillandsia for sure. They love humidity and they take in water through their leaves. They anchor themselves to a substrate with their roots. The plant itself can be tied to it's substrate or attached to it with a dab of hot glue or silicone adhesive. Once the plant is established and growing it will begin generating fresh anchor roots on it's own.
I'm not certain about the lighting requirements for your Tillandsia. I have one that has a similar bloom but different plant structure than yours. Mine is thriving outdoors in low level dappled sunlight with daily mistings using ordinary tap water. When watering I concentrate on saturating the plant with less emphasis on watering the roots. My plant doesn't seem to suffer any ill effects when I skip a few days between waterings and it blooms repeatedly throughout the year.
I have no complaints when it comes to Tillandsias. They're neat little plants, a joy to the eye, and practically care free.