Measure the basement wall you will cover with the new wall.
Cut the 2-by-4-foot pieces of wood to create the frame. You will need a base plate and a top plate, which measures the length of the wall, and one vertical piece for every 2 feet of length for the wall. The vertical pieces fit between the base plate and top plate and give the wall its height. Leave at least 2 inches from the floor joists to the top of the wall to accommodate a ceiling later.
Piece the frame together on the floor. Lay the top and base plates parallel to each other, but perpendicular to the floor. Place the vertical pieces between the two plate pieces, nailing each one in place about 2 feet apart.
Set the wall frame against the cement basement wall.
Insert wood shims between the floor joists in the basement ceiling and the top plate on the wall frame.
Drill a hole through the top plate, the wood shim and into the floor joist above.
Secure the top plate to the floor joists with wood screws.
Drill holes through the bottom plate to give you access to the cement floor beneath the plate.
Change to a masonry drill bit and drill pilot holes into the cement underneath the bottom plate.
Insert masonry screws through the bottom plate and into the cement floor to hold the bottom of the wall frame in place.