Orchids require very little pruning. Usually only when the old flower spikes die off, when dividing the plant, or when repotting do you need to prune. Proper plant identification helps when deciding when to prune and what parts of the plant you need to prune, if any. Many orchids will naturally drop old leaves and do not need to be manually removed.
Many orchids will only bloom once per flower spike, while others will rebloom or can be forced to rebloom from the same spike. It is best to know exactly what type of orchid you have before attempting to prune dead flower spikes.
For flower spikes that do not rebloom, let the stalks dry back to the plant and cut them as close to the plant as possible. It's OK to leave a stub if you can not reach in between leaves.
For types that will rebloom on the same flower spike such as Phalaenopsis, you can cut the spent flower spikes back to just about a quarter-inch above the top node and it may rebloom. Some types will rebloom continuously on one spike without any pruning.
When doing a regular repotting, use a sharp knife razor or shears to remove any dead or rotting roots. These roots, if left on, will break down fast and can potentially be a source of fungal or bacterial infection in the plant.
Most growers leave a leaf on the plant until it has completely yellowed and died. Usually it is easy at this point to give the dead leaf a gentle tug and it will break away from the plant at the correct point. Other growers choose to cut them off before they have died completely.
When dividing sympodial types make sure to leave at least two or three growths and or back bulbs and a few roots per division. Many monopodial types can be topped right below where new roots sprout from the stem and the top can be repotted.
Sanitation must be kept in mind when pruning orchids. If you are cutting several plants it is a good idea to sanitize the razor or shears with rubbing alcohol or with a torch in between pruning plants. This prevents the transmission of harmful bacteria, fungus and orchid viruses.