Measure the height and width of the wall to be framed. Cut two 2-by-4-inch boards to match the width. These serve as the top and bottom plates for the frame wall.
Divide the width of the wall, in inches, by 16. Round this number up and add one. This is the number of vertical studs that will be required in the frame wall. Cut the proper number of studs, each stud measuring the height of the wall, minus four inches.
Place the top and bottom plates parallel to each other on the floor, resting on the narrow edges. Arrange the studs perpendicularly to the plates, starting at one end, and spaced 16 inches apart, measuring from the center of each stud. Place the last board even with ends of the plates at the other end, regardless of the distance if it's less than 16 inches. Nail the studs to the plates with two nails at each point where the studs meet the plates.
Raise the frame wall so it's vertical, and slide it into position against the poured wall. Nail the bottom plate to the subfloor in between each of the vertical studs. Slide shims between the top plate and the points where they intersect with the ceiling joists. Nail through the top plate and the shims, into the joists.