Measure the distance from the top of the support wall's bottom plate to the bottom of the box opening. Cut two pieces of 2-by-4 lumber to match the dimension, less 1 1/2 inches. These are the jack studs that will support the box frame. Place the jack studs on the insides of the vertical studs on either side of the box opening location. Nail the jack studs to the studs with 10d nails every 6 inches. If your opening needs to be greater than 14 3/4 inches, you'll need to cut the existing studs at the height of the box opening, less 1 1/2 inches. Then install new vertical studs to either side of the opening and place your jack studs to the inside of these. The footer board installed in the next step will rest on top of the jack studs and the remains of the original studs.
Measure the distance between the inside edges of the two studs on either side of the jack studs. Cut three pieces of 2-by-4 lumber to match the distance. Place one piece on top of the jack studs, broad side down, and nail to the jack studs with two nails on each side. This is the footer for the box frame. Save the other two pieces for later -- they are headers for the box frame.
Cut four pieces of 2-by-4 to match the height of the box opening. Two of these will be additional jack studs for the box opening and two will be the outer sides of the box frame. Place two of the jack studs against the studs on either side of the box opening location, directly above the first two jack studs and on top of the footer. Nail them to the studs with 10d nails every six inches.
Place the header boards on top of the two jack studs, broad side down and one on top of the other, nail the lower header to the tops of the jack studs with two 10d nails on each side, and the top header to the bottom header with two 10d nails on each side and an additional nail every six inches.
Place the other two 2-by-4s from Step 3 between the footer and header at the proper spacing for your box frame. Nail them to the footer and header with two nails at each intersection.
Measure the distance between the top of the top header board and the bottom of the top plate. Cut 2-by-4s to match the distance and nail in between the top header board and the top plate at a 16-inch spacing on center.