Determine where to place the half-wall and the half-wall's size. One end of the half-wall should adjoin a stud in an interior or exterior wall. Use a stud finder to locate the wall stud.
Mark the length of the half-wall on two 2-by-4-inch lumber sections. Cut the lumber to that length using a circular saw. The sections will form the half-wall's top and bottom plates.
Measure and cut 2-by-4-inch lumber sections to a length 3 3/4 inches shorter than the finished height of the half-wall. These sections will form the half-wall's studs. One stud is needed for each end of the wall, and a stud is needed for each 16 inches of wall length.
Assemble the half-wall frame by laying out the top and bottom plates on their 2-inch sides and placing the studs between them. Place the studs so they are 16 inches on center, which means the center of each stud is 16 inches from the center of each adjacent stud. Drill pilot holes through the top and bottom plates into the ends of each stud, and insert 4-inch long wood screws into the holes with an electric screwdriver to secure the plates to the studs.
Stand the half-wall frame in your desired location. Check the half-wall against the adjoining wall with a carpenter's square to ensure the half-wall is square. Mark the flooring around the bottom plate.
Remove flooring such as carpet or ceramic tile within the mark you made around the bottom plate. The half-wall should sit directly on the subfloor.
Drill pilot holes through the bottom plate into the subfloor. Secure the bottom plate to the subfloor with 4-inch long wood screws. Secure the half-wall to the adjoining wall by driving 4-inch long wood screws through the end stud into the adjoining wall stud at 4-inch intervals.
Cut drywall sheets with a utility knife so they fit the sides and exposed end of the half-wall. Attach the drywall to the half-wall's frame with drywall screws.
Cut a section of 1-by-6-inch lumber to a measurement that is 1 inch longer than the half-wall. Place that lumber section on the half-wall's top plate so that one end meets the adjoining wall. This lumber section should extend beyond the half-wall by 1 inch on the sides and the end opposite the adjoining wall. Secure this top section to the top plate with 2-inch long finishing nails.
Measure and cut base molding to fit around the bottom of your half-wall before spackling, taping, sanding and painting the drywall for a more finished appearance. Secure the base molding to the half-wall with 2-inch long finishing nails.