Figure out the height and width of the wall you want to build. Create a mock-up of the wall by cutting cardboard pieces to your measurements. Assemble them and position them in your space to see if the size is appropriate.
Use four two-by-fours to construct the frame for your half wall. A lumber yard will cut the lumber to your specifications. Use wood screws and an electric screwdriver to join the pieces.
Attach the frame to the existing wall with additional wood screws. Use a stud finder to locate the wall studs to attach the frame to the wall securely.
Cut the wall board to fit the dimensions of the sides of the frame. Use a utility knife to score one side of the paper on the wall board. Stand the wall board up and break it along the score line. Repeat on the other side of the wallboard and break the wallboard cleanly.
Attach the wallboard to the frame using nails. Cut a narrow piece of wallboard in the same manner to cover the exposed end of the frame.
Attach metal corner strengtheners with metal tacks to reinforce the exposed edges of the wallboard.
Apply a thin bead of joint compound to the seam between the half wall and the existing wall. Cover the seam with paper tape. Dip the tape in water and remove excess water by running the tape between your fingers and thumb. Press the tape into the seam keeping it flat and smooth.
Use joint compound to conceal the ridge created by the metal strengthener and the wallboard. Blend it for a smooth surface. Allow the compound to dry and apply a second coat. Sand the area when it is completely dry.
Use a poplar board to create a shelf for the top of the half wall. A lumber yard will cut the board to your specifications. Secure the board to the top of the half wall with nails. Cover the nail impressions with spackling compound to smooth the surface. Sand the area as needed.
Use wall primer to prepare the half wall for painting. Apply two coats of latex wall paint to all surfaces. Allow the paint to dry thoroughly between coats.