How do I grow orchids hydroponically?

Why exactly would you want to grow them hydroponically? Most commercially available orchids are epiphytes, and don't grow in soil. They (again, for the most part in a commercially available sense) have spongy roots that can store water, and are generally potted in a mixture of bark, moss and other materials, sometimes even just volcanic rock. This potting medium acts as a way to keep humidity around their roots, humidity being the most difficult factor to control in a typical home environment. Your best bet is to go to a book store and find a beginner's book. In my experience, Phalanopsis (moth orchids) and Paphiopedilums (slipper orchids) are the easiest to grow in a home situation. Of course, If you live in a warm, humid climate, you have much more options. I've found that orchids are near indestructible- it's getting them to flower that's the tricky part. In general, bright indirect light, humidity, warm temperatures, and air movement are the key common factors. Just look them up in google. There's a huge amount of info available online. You're probably going to be more limited by the kind of orchids you can buy in your area than any other reason.

You'd be a lot better off, trying to find and become friends with http://www.google.com/search?hl=en&q=orchid+clubs&btnG=Google+Search, than reading books. All the best cultivars, and most of the best knowledge, in the orchid world are passed mouth to ear. But I agree with jeff-o-matic; culturing orchids hydoponically is for the birds. If you like orchids, forget that, right now. Your challenge as a hobbyist is to gently convince the objects of your desire that you've taken them to Costa Rica for vacation, a couple times a year, and hope they believe you and, literally, put out. A mentor who can look at your plants, and show you his/hers, is worth 500 multi-color photos in a widely bought book. Put it this way: if you were having marital troubles, would you buy a book, or find a knowledgeable person?

If you really are interested in growing orchids, some are much more challenging than others. A really good starter species is http://paphiopedilums.netfirms.com/ (the "lady slipper"). I have a black thumb and I managed to make one bloom three times, sitting on my desk at work in a cube farm, living solely off the flourescent light from the ceiling fixtures. http://www.orchids.mu/Species/Odontoglossum/index.html (the "butterfly orchid") is also supposed to be easy to grow, and they're a lot more beautiful. But I have no personal experience with that species. What's nice about both of these species is that their natural growing environment is cool and dry and not very bright, which means that they like the same conditions that you do and don't have to be pampered with high heat or humidity in order to fool them into thinking they're in Costa Rica. And they don't like or need direct sunlight, which also makes them easier to care for. But the other posters are correct: orchids are just about the worst possible choice for hydroponic growing.