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, gray 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 discolored 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.