Orchids all have a long period of blooming, and an equally long period of rest. Once all buds have bloomed and dropped off the plant, do not cut off the bloom spike--some varieties, notably Phalaenopsis species--will re-bloom on a shoot that arises off the previous bloom spike. In all orchids, only cut back bloom spikes if they are clearly dry, brown and repleted.
When your plant has entered its rest period, give it the same light and temperatures as it enjoyed while blooming, and water as needed, which is usually less often than it needed while blooming. Check the moistness of the potting mixture with a fingertip and water as needed to keep some moisture present at all times. Never allow an orchid to stand in water--use a drain pan under the plant that contains pebbles, or water in a sink, then put the plant back in the saucer when it has stopped dripping.
You may do as I do and "retire" your resting plants to another windowsill where they can enjoy peace and quiet but not be so prominently on display. While not an ugly plant, a resting orchid is certainly not as lovely as during its bloom cycle, so many of us put the resting plants into a spare room.
As soon as you see a new flower spike emerge from the base of the plant or from an existing spike, begin training it by clipping it to a flexible wire support with an orchid clip. This will prevent the flower spike from drooping over the side of the pot (Some growers prefer their plants to show their natural form and leave the flower spikes to trail; this is a matter of personal preference.)
Depending on the species, your orchid may bloom for a period of a few days to six months or more. Rest periods also vary family to family but in general expect your plants to rest from two to six months. Be patient; you will be rewarded with months of blooms!