Measure the height of your basement from floor to ceiling, and the depth from the wall to the edge of the ductwork. Cut four 2-by-2s to the length you need.
Measure the elevation of the bottom of the floor joists to the bottom of the ductwork and add 1 ½ inches for clearance, deducting 3 inches. This is the length of the vertical pieces for the side of the ductwork. For example, if the ductwork is 10 inches, then 10 inches added to 1 ½ inches take away 3 inches equals 8 1/2 inches.
Nail the 8 ½-inch verticals between the top and bottom plates at 24 inches on the center to build your square box---which will begin to look like a ladder. Build one for each side of the ductwork.
Raise your frame and nail each ladder with a hammer to the wall and ceiling joists---one on each side of the ductwork. Use a level as you go to make sure they are square and plumb.
Cut pieces of 2-by-2s and screw them every 24 inch on center between the two ladders. You can now use the ladder frame around the ductwork to place your drywall over and confine the ductwork.