Shop for a vacuum filter specifically designed to handle drywall dust. Retail hardware stores typically carry suitable filters for a variety of popular shop vacuums, but you may need to contact the vacuum manufacturer directly to obtain a new filter that fits your model.
Unplug your shop vacuum and remove the existing filter. Typically, this requires undoing several latches to lift out the vacuum motor. Unfasten any screws holding the filter in place and set it aside for future use during projects that don’t involve drywall dust.
Install the new filter. Follow the manufacturer’s directions for the new filter to ensure it remains effective and keeps dust within the chamber. For example, remove and clean the filter as soon as the vacuum's suction significantly decreases.