The vast majority of orchids grown in the home are epiphytes, meaning they live in nature by clinging to trees or even stones. The roots of these plants are highly specialized organs that differ dramatically from normal plant roots. Of course, it's hard to generalize about anything when it comes to orchids. This is the single largest group of plants in the world, so for every rule, there are 100 exceptions.
Orchid flowers are all bilaterally symmetrical with three petals and three sepals. Their seeds develop in capsules and are extremely tiny, sometimes mistaken for dust or spores. Because the seeds are so small, they don’t contain enough nutrition to grow a new plant themselves, so they develop a symbiotic relationship with fungus, which provides the nutrients for them to grow.
Masdevallia is one of my favorite types of orchids! They have triangular flowers (the petals are tiny, so you just see the three sepals.) They need cool temperatures to do well, and like a lot of humidity, but are otherwise quite easy to grow. (But they have a reputation as being hard to grow from people who've ignored their temperature and humidity requirements.)
Another type of orchid you can grow at home is what I call the “Thai restaurant orchids.” These types of orchids are Dendrobium hybrids and can be found at Thai restaurants that decorate their tables with freshly-cut flowers. They come in many colors (white, green, purple, pink, yellow and more) and require a fairly warm environment. In fact, they could loose their leaves in the winter when the ambient temperature drops below 60°F (15°C) or so. But the “Thai restaurant orchid” is really just one small group of hybrids within the Dendrobium genus. Dendrobium is actually one of the largest orchid genera.
Water thoroughly. When you do water, do it like you mean it. Different growers have different rules, but many professional growers turn on their sprinklers for 8 or more minutes. Successful home-growers sometimes dunk their plants, pots and all, into a bucket or sink of water. Some varieties, such as vandas, can be left floating in water for a surprisingly long time. The idea is to make sure the velamen is completely saturated. You want tiny droplets hanging on the roots after watering. This means the plant is completely hydrated.