Measure the width and the height of the wall. Cut two 2-by-4-inch boards to match the width of the wall. Place these boards on the floor, sitting on their narrow edges and parallel to each other. Slide them apart until they're separated by the height of the wall's distance.
Cut a series of 2-by-4-inch boards to match the height of the wall, less 3 inches to account for the top and bottom boards. Cut enough boards to place one board on each end and place studs at 16 inches along the wall.
Place the vertical studs in between the parallel top and bottom boards, spaced 16 inches apart. Place them against the parallel boards and nail the boards together where they intersect.
Raise the wall and move it into place against the basement wall. Nail the bottom board into the sub floor and the top board into the ceiling joists at the points where they intersect.