Measure the distance from the basement floor to the bottom of the ceiling joists and then add 3 inches to that measurement. This will be the length to cut your 2-by-4-inch wall studs.
Cut enough 2-by-4-inch studs, using the measurement you arrived at in Step 1, to cover the wall when the studs are spaced 16 inches apart, measuring from the center of one stud to the center of the next stud. This measurement is also called “16 inches on center.”
Nail the studs to a 2-by-4-inch top plate and a pressure-treated, 2-by-4-inch bottom plate. Drive two nails into the ends of the wall studs, driving them directly through the top and bottom plates into the studs.
Stand up the completed section of wall, positioning it so the top plate is snug against the bottom of the ceiling joists and the bottom plate is snug against the basement wall.
Attach the top plate to the ceiling joists with 3-inch wood screws. If there is a small gap between the top of the top plate and the bottom of the floor joists, insert wood shims to bridge the distance and then install the screws through the shims, into the floor joists.
Drill two holes on the bottom plate, evenly spaced between each upright stud. Use a drill with a concrete hammer bit and drill down about 2 inches below the surface of the basement floor.
Install 3-inch masonry screws into the pre-drilled holes in the bottom plate. This will secure the wall to the floor.