Remove any wall covering around the duct work down to the studs. This will allow you to gauge where to place the studs around the ducts.
Measure the duct work. If it's below the ceiling, you'll need to create a wooden cage to enclose it that attaches to the joist and the studs. If it's upright in a corner, you can simply box it in.
Be sure that there will be adequate headroom for people to walk below the duct work. Allow half an inch between the duct and the boxing to prevent vibration in the duct work causing it to hit against the wood.
Measure and cut two-by four lumber for the length of the duct to make a frame. You'll need four lengths unless it's in a corner, in which case only cut three lengths.
Mark on the walls where the frame will meet the wall and measure the distance from the nearest studs. Cut lengths of two-by-four lumber to fit between the joist and the top lengths of the frame. Screw in place along the joist, working in 24-inch centers. Screw the top stud of the frame to these pieces, using a level to keep it straight. Repeat on the opposite side.
Measure to establish the distance between the upper and lower studs in the frame and cut lengths of the lumber to the correct size. Screw in place on the upper studs on 16-inch centers. Attach the lower studs to the lumber with screws.
Measure the distance between the two lower studs and cut lumber to fit between them. Screw in place on 16-inch centers. Box in the frame with either drywall or plywood to complete.
Screw or nail battens in place between the studs behind the duct work, the battens being in 16-inch centers. Measure where the frame for the box will sit and attach two-by-four lumber to the battens, screwing in place. Measure the distance from these pieces to the corner piece that will protrude into the room.
Cut two pieces of this length. Attach one at the bottom, along the floor and the other at the top, at the ceiling. Screw into floor and ceiling for stability. Screw the remaining piece of the frame to these, then repeat the process on the other side.
Measure and cut battens for the sides and screw these in place to the lumber on 24-inch centers. Repeat on the other side before boxing in the duct work with drywall or plywood.