Water
The first thing to consider is how much water you give your orchid; orchids naturally grow in exposed environments and it's easy to keep their roots too wet when they're potted. The most common mistakes that get made are either watering too often (and thus always keeping the roots wet) or not watering thoroughly enough (so the roots don't drink enough water).
One common way to water your orchid is to take it to the sink, remove the decorative pot (not the plastic pot holding the plant that has drainage holes), rinse all the roots and potting mix with tepid water (even ones outside the pot) very thoroughly (10 seconds or so), and then wait about 1 week until watering again once the potting mix gets dry and light. If it's in a transparent pot, the roots should turn silver before watering; if they're still green, then that means the roots are moist and can be left alone.
If you're having trouble determining if an orchid needs water, here are some references: are the leaves thick and fleshy but limp or supple? (or if the plant has grassy leaves, are the stems/bulbs becoming more wrinkled than normal, and look shriveled?) then they need a very, very thorough watering (in these cases I let the plant soak overnight to plump up the leaves, and then let the plant dry again before watering). Is the potting mix still heavy and dark? then keep waiting. Are the leaves yellowing from ends or starting to brown? then the plant is staying too wet and needs to dry out faster or longer.
In some cases, orchids are planted into a pot without drainage, which means that any water that is added can sit around the roots until either it slowly evaporates or the roots drink it. Unfortunately, orchid roots don't have the ability to handle staying damp, so this usually causes the roots to rot. If you have an arrangement like this, then you can add a small amount of water every week ( say one ounce or 30 mL ) to each plant, and then once the flowers are done blooming, you can take apart the arrangement to put each orchid into a pot with drainage and use the above guidelines for watering.
Light
Most orchids are shade growers, which means they grow under the shade of other plants, not that they don't like direct light. This means that in the wild they're protected from midday sun from above but receive indirect light all day and morning or afternoon sun. East and West-facing windows are often good light sources for orchids, and being next to the window means that the orchid can produce enough energy to grow well and then flower. If the light is too dim or short-lived, then it can mean that the plant takes longer to grow and gather the energy to flower again.
You can use a light meter or download an app on your phone to measure the strength of the light, and in general, a good window should let through 1500 foot candles or (16000 lux) of light intensity.
You can also grow many orchids under artificial lighting, in some cases even better than under natural light, since you have better control. The simplest way is to set the lights on a timer of twelve hours on, and twelve off, and with the availability of LED lights, you no longer need to worry about burning leaves by putting the lights too close.
More Specific Care Guides:
Oncidium types hybrids
Ovaloid pseudobulbs with one to two leaves at the tip, and two leaves at the base, flowers in a spray
Dendrobium:
e.g. Mini Snowflake, Micro Chip, Roy Tokunaga
Dendrobium section
D nobile hybrids, soft leaf, often deciduous, sometimes require a winter rest
Dendrocoryne section
Australian Dendrobiums like D. kingianum, usually fragrant and many color forms
Calyptrochilus section
Small plants with large, long-lasting flowers, related to D cuthbertsonii and laevifolium.
Dracula:
Sometimes called monkey-faced orchids, they were originally classified as Masdevallias but grow rather differently. They have soft, pliable leaves with a pointed tip, and many bloom downwards.
Phragmipedium:
Tropical American lady slippers, different from Asian lady slippers in their environment and how they bloom; most Phrags bloom sequentially, with a long season of single flowers on each stem.