Cut pressure-treated 2-by-4 boards to fit along the base of the concrete wall. These will be used as sill plates. The sill plates are used to connect the framing to the floor, and help protect the frame from rotting as the chemicals used in the pressure-treating process are resistant to water damage.
Drill pilot holes every 12 inches into the floor where you're placing the sill plates using a masonry drill bit.
Screw the sill plates to the floor with masonry screws.
Stack two 2-by-4 boards on top of the sill plates and measure the height of the wall between the 2-by-4s and the ceiling joists. Use this measurement when cutting the studs for the wall frame. Don't nail the 2-by-4s to the sill plates; you place them there because when measuring the height of the wall studs, you need to take into account the thickness of the top and bottom plates of the framing; otherwise you may cut the studs too long.
Cut the top and bottom plates for the frame so they match the length of the sill plates. Use untreated 2-by-4 boards for the studs and top and bottom plates.
Cut 2-by-4 boards to fit the height needed for the studs. The standard spacing between studs is 16 inches, but follow your local building codes when framing the wall.
Nail studs into the bottom plate, spacing them according to your local building codes. Complete the frame by nailing the top plate to the top of the studs.
Lift the wall frame into position on top of the sill plates. Check to make sure it is plumb (vertically straight) and level (horizontally straight). Nail it to the sill plates and the ceiling joists. You may need the help of an assistant when doing this.