Gloria, you can also find some useful information on the Cymbidium Society of America's website:
Cymbidium Society of America: Cymbidium Culture
Depending on what kind of cymbidiums you bought (species or hybrids, standard-sized or miniature asian varieties, etc.), the care will vary a little. But, in general, the vast majority of cymbidiums that are widely grown today are large hybrids that like to have a moisture-retaining potting mix (small-grade fir bark, perlite, a little chopped sphagnum moss, etc.) that's free-draining (avoid typical garden soil). They produce massive root systems, but make sure that your pot is sized correctly for the plant (just big enough for maybe a couple of years of growth). After you pot your plants, put them in a relatively shady location. If the light's okay for your phals, it should be fine for the cymbidiums until they get established and produce new growths and new roots. Keep them a bit on the dryish side too after they get potted up. Once they start producing their new growths and roots and become established in their new pots, however, they're going to need a lot more light than what keeps phalaenopsis happy, and they'll want to be watered and fertilized regularly (I don't let my cymbidiums get completely dry during the growing season like the cattleyas get). They can actually handle more light than most cattleyas. But the trick for you will be to balance light levels and high temperatures. If your growing area experiences really high temperatures, you're not going to be able to give your cymbidiums the same light levels that growers in traditionally cymbidium-friendly areas of the country like San Francisco and the Pacific Northwest routinely give theirs (keep that in mind when you're reading the CSA's cultural information page, which was written primarily with these growers in mind). Best of luck with your plants.
Steve
Help with my first Cymbidium
They will arrive bare-root some time next week and I need a little advice on potting and initial care. 
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