Cymbidium is a species of large flowering orchid plant, considered to be the most cold hardy of common orchids. Cymbidium orchids are terrestrial and can be grown out of doors in many temperate climes. Like all orchids, pruning requirements for cymbidiums are fairly minimal, as the plants are evergreen. Proper pruning is as much about what you don't do as much as what is helpful to the plant.
Deadhead any completely spent bloom spikes after they begin to wilt and look tatty. Sever the stem at the base between the leaves, and discard it.
Cut off any dead roots that are protruding from the top of the pot. Identify dead roots by their hollowness, grey or brown hue and dessicated, soft texture. Refrain from cutting into any white roots, as these are healthy live tissue.
Inspect the plant foliage for any dead, badly discoloured or diseased leaves. Snip off the problem leaves down at the crown of the plant just above the slightly swollen pseudobulb that emerges form the soil. Dead or diseased leaves will often release from the plant when touched lightly, and this is an acceptable method if they are loose, but do not tug on or tear the leaves, as this can damage the plant.
Cymbidium flower spikes can be used as long-lived cut flowers if you're willing to sacrifice them from the plant. Wait until roughly half of the blooms on the stalk have begun to open and sever the bloom spike down at the base of the stem between the straplike leaves with a sharp, clean cutting tool.