Apply the Drywall
Using a utility knife, cut the 1/2" drywall to fit the half wall. Secure the drywall to the studs with the screw gun and 1-1/2" coarse drywall screws. Keep the top edge of the drywall flush with the top of the top plate. Fill the screw holes with joint compound, let dry, then sand smooth.
If drywall is applied to both sides of the half wall, the total thickness of the wall will be 4-1/2". Rip the 1" x 6" down to a width of 5", which will give a 1/4" overhang on each side. Cut and attach the 1" x 5" clear pine to the unfinished top and end of the wall. Cut the end of each board at a 45-degree angle where they meet at the corner. Attach the 1" x 5" pieces by face-nailing them into the exposed 2x4s with the 18-gauge nail gun and 2" nails. Apply wood putty to the nail holes and sand smooth.