Use a tape measure to mark the new wall, measuring from the existing wall. Snap a chalk line along the marks (Image 1).
Then measure from the ceiling to the floor joist above to determine the length of the studs (Image 2). Subtract 3" from that measurement to account for the top and bottom plates -- one 2x4 on top and one 2x4 on bottom.
Use the measurements taken earlier to mark the 2x4(s) with a speed square (Image 1), and cut the boards to length.
When the boards are cut, lay out the pieces: one on the top and one on the bottom, and a board perpendicular at every 16" on center (Image 2).