Measure the height and width of the stem wall with a tape measure and record the measurements. Divide the width of the wall, in inches, by 16 and add 1 to determine the number of vertical studs you'll need for the frame wall.
Cut a series of 2-by-4-inch boards to match the number determined in the previous step. Each board should measure 4 inches less than the height of the stem wall. Set the studs aside.
Cut two 2-by-4 boards to match the width of the wall. These are the top and bottom plates of the frame wall. Place the top and bottom plates parallel to each other on the ground, resting on the 2-inch sides. Arrange the vertical studs between the plates, perpendicular to the plates, so that the ends of the studs butt up against the plates. Place the first stud even with the ends of the plates, then space the boards 16 inches apart, measured from the center of each stud. Place the last board even with the other end of the plates. Nail the studs to the plates with two 10d nails at each point where they meet.
Raise the wall and slide it into position against the stem wall. Nail the bottom plate to the sub floor with a nail between each of the vertical studs. Nail the top plate to the joists above the frame wall with a nail at each point where the joists cross the top plate.