Place the duct register over the duct, inserting the inside of the register into the duct. Hold the register against the drywall and mark the mounting holes with a pencil. Remove the duct register from the duct and set it aside.
Put a drill bit that is the same diameter as the plastic anchor into your drill. Drill two holes in the drywall at the mounting hole marks.
Push the plastic anchors into the pilot holes. Tap the plastic anchors lightly with a hammer until the top of the anchor is flush with the drywall.
Insert the duct register into the duct, lining up the mounting holes with the anchors. Thread screws through the mounting holes and into the anchors. Tighten the screws with a screwdriver.