Wait until the orchid stops blooming entirely before you attempt to cut it back. In general, when the stalks begin to the turn brown, it is time to begin trimming.
Remove all stakes and other support structures from the orchid pot so that you have plenty of room to perform the pruning process.
Grasp one of the center stalks that is completely brown or yellow. Trace it back to the center of the plant as close as you can to the soil line. Cut the stem off using hand pruners. Prune off all remaining dead stalks in the same manner.
Remove any stakes or trellises from the orchid pot to make room for pruning.
Sterilize your hand pruners to prevent disease from forming in the healthy plant tissue. Sterilize the blades by holding them under the end of a small butane torch. You can also wipe them with a cloth soaked in rubbing alcohol.
Trace the stalk down to the base of the plant and then move up until you see a raised ridge around it called a node. Move up to the second node and cut the stem off 1/2 inch above it with the sterile hand pruners.
Place 1 tbsp. of powdered fungicide into a small cup. Add 1/4 tsp. of water and stir the powder with a cotton swab until it forms a paste. If needed, add more water one drop at a time until the mixture looks like toothpaste.
Scoop up some of the paste on the tip of the cotton swab and dab it onto the cut end of the orchid stem.