Mark the location of your half-wall on the floor. Use a chalk line to snap a line of chalk onto the floor for the length of the wall and across the wall at both edges for the proposed half-wall width. Make the half-wall 16 inches wide if possible to place the frame into the wall studs. Place an additional line on the wall at the desired height of the half-wall. Measure the length, width and height lines with a tape measure to determine the dimensions of your half-wall frame.
Mark the measured length of the wall onto two of the 2-by-4-inch planks and cut the planks to serve as the top and bottom plates of the wall. Subtract 3 inches from the height measurement and cut two 2-by-4 planks to match the adjusted height measurement.
Place the short height boards between the top and bottom planks at the edges of the planks to create a rectangular frame. Attach the boards together using a pneumatic framing gun with 10d nails through the long plate boards, into the short height boards at either end of the frame, using two nails per joint.
Make a mark with a pencil along the frame every 16 inches from the edge of the frame closest to the wall. Cut a 2-by-4-inch height plank for every mark. Place the plank between the top and bottom planks and nail them into place to create wall studs to connect paneling or drywall to the half-wall.
Make a second frame for the other side of the wall, following the same steps as for the first frame.
Subtract 3 inches from the width measurement and cut four 2-by-4-inch boards to the adjusted measurement. Place the width boards between the two frames at the top and bottom of the frames, and nail them into place. Cut two additional width boards for each of the stud plank locations. Position the width boards along the top and bottom plates of the frames, between the frames, and nail them into place for additional support.
Place the frame against the wall and nail it into the subfloor through the bottom plates on both sides of the wall frame, spacing the nails every 10 inches. Nail the frame through the drywall and into the wall studs through the sideboards of the frame.