Build a wooden frame around the duct work that you are hiding. Two-by-three lumber is sufficiently strong for the corners of a duct-hiding construction. You may use simple one-by-three furring strips to fill in between the corners and provide a screwing surface for the drywall. Assemble the wooden frame with screws to avoid banging against the duct with a hammer. Make the frame so it is as close to the duct as possible without touching it. A duct in a corner or next to a wall can be concealed with an L-shaped frame connected to the ceiling and wall; a duct that protrudes out of the ceiling at the center of the room will need a U-shaped frame to hide it.
Measure the faces of the box you have constructed and cut pieces of drywall to fit these areas. Screw the pieces of drywall onto the structure using 1¼-inch-long drywall screws.
Screw metal or plastic drywalling corners onto all outside corners. These are rigid L-shaped strips that are designed to reinforce the corners and help you to end up with a straight and attractive line.
Cover the outside corner strips, screw head holes and joints between drywall pieces with spackle. Apply drywalling tape to all inside corners and joints between drywall pieces. Allow the spackle to dry for 24 hours.
Sand the spackle dry. Apply primer to all the surfaces of the new construction. Finish paint the walls and ceilings to match sorrounding walls and ceilings.