Measure the length, width and height of the duct with a measuring tape. Cut four sections of 2-by-2-inch lumber to the length of the duct with a circular saw.
Cut sections of 2-by-2-inch lumber equal to the height of the duct to form the side studs. You need two studs for each end of the soffit, plus two studs for each 16 inches of soffit length.
Set one pair of length sections parallel on the floor. Place one stud perpendicular between the length sections at each end, and at 16-inch intervals between the end studs. Insert 4-inch wood screws through the length sections into the ends of the studs with a drill and a screwdriver bit. Repeat this process with the remaining length sections and studs.
Position one soffit side 1 inch from the duct on the basement ceiling joists. Attach the soffit side to the joists with 4-inch wood screws. Repeat this process with the other soffit side.
Measure the distance between the bottom sections of the soffit sides. Cut sections of 2-by-2-inch lumber to this measurement. These sections form the bottom frame of the soffit. You need one section for each end of the duct, plus one section for each 16 inches of soffit length.
Place a bottom frame section between the bottom length sections at one end of the soffit. Insert 4-inch wood screws through the bottom length sections into the end of the bottom frame section. Repeat this process at the opposite end of the duct, and at 16-inch intervals between the end bottom frame sections.
Cut drywall sections to fit the sides and bottom of the soffit frame with a utility knife Attach the drywall sections to the frame with 2-inch drywall screws.
Tape the corners and seams of the soffit frame with drywall tape. Apply drywall compound to the tape edges and screw heads with a putty knife and allow it to dry overnight. Sand the drywall with a palm sander to smooth out the compound.