Soak a cotton ball in hydrogen peroxide. Run the cotton ball along the cutting surface of a pair of pruning shears to sterilize. Allow the shears to air dry before proceeding.
Use two fingers to gently spread the blossom stalk away from any neighboring blossom stalks to avoid trimming off potential blooms.
Position the cutting surface of the pruning shears around the spent bloom stalk, 1 inch up from where it meets the main stalk of the orchid. Hold the shears so the blades are at a 45 degree angle to the bloom stalk. Snip firmly to clip off the spent bloom stalk cleanly.