Use a stud finder to locate the stud in the intersecting wall that is closest to where you're framing the half wall.
Cut the molding from the base of the intersecting wall so you can butt the end of the half wall directly against the intersecting wall.
Cut a pressure-treated two-by-four board that matches the length of the wall. This board is the sill plate, which will connect the framing to the floor.
Lay the sill plate onto the floor with one end against the wall where you removed the molding, and drive screws through the sill plate and into the floor every 6 inches.
Cut two standard two-by-four boards that match the length of the sill plate. These boards will be used for the top and bottom of the framing, and are called the top plate and bottom plate.
Divide the length of the half wall by 16 to determine how many studs you need for the wall. You divide by 16 as the standard spacing for wall studs is no more than 16 inches.
Nail a stud to each end of the bottom plate.
Nail studs between the two end studs, keeping them spaced no more than 16 inches apart.
Lay the top plate across the top of the framing, and nail it to the top of the studs.
Place the assembled half wall frame on top of the sill plate, with one end against the intersecting wall.
Check to make sure that the framing is straight, and nail it to the sill plate and the intersecting wall.