oh no wait until the flowers have faded. spritzhenry has done an excellent blog on orchid care. well worth a read Niles.
welcome to GoY.

Which type of orchid is it?

If it's a Phalaenopsis, I'm finding that mine aren't enjoying the low light levels at this time of year, plus the house temperature varies a fair bit (as the heating is on a timer). Are the flowering stems continuing to grow beyond the last flower? If so, leave the stems alone as they will continue to produce blooms later on. If not, follow the advice of Spritz about cutting them back.

If it is something else (Dendrobium, 'Cambria', Oncidium), then check further down the stems for side shoots before cutting off. My experience of these is that side shoots only form whilst the spike is actively blooming, but will not start after the spike has finished blooming, so cut these off as near to the bottom as you can.

One last point; it's especially important to keep the humidity up at this time of year. Misting every morning is good, plus standing them in a tray lined with pebbles that has water in it to just below the top of the pebbles. If you have more than one keep them bunched up.