Measure the area for your basement bedroom to determine the amount of materials you require. Allow 4 furring strips and 1 sheet of drywall for every 4 feet of wall space. Measure the wall that will enclose your bedroom from the rest of the basement. Allow four 2-inch by 4-inch pieces of lumber for every 4 feet of space along this framed wall. Leave room for the type of door that you have chosen.
Attach pressure-treated 2-by-4-inch sections of lumber along the bottom and top walls of the foundation. Use a hammer drill and concrete screws to attach these to the concrete. Create the bottom frame of the wall that closes off the rest of the basement in the same manner, stopping at the doorway opening. Attach the top 2-by-4-inch sections of lumber to the exposed floor joists overhead.
Attach the furring strips to the concrete wall, placing them on 16-inch centers. Use a level to place the strips vertically on the walls. Connect these directly to the foundation walls with concrete screws. Finish framing out the interior wall by using 2-by-4-inch pieces of lumber, nailing these to the top and bottom pieces of lumber every 16 inches.
Cut insulation panels to fit the spaces between the furring strips. Attach these to the foundation walls with insulation adhesive.
Contact a licensed electrician to install your electrical wiring at this point.
Nail the drywall sheets to the furring strips and the framed wall that closes off the rest of the basement. Cut and fit the sheets to create seams over the centers of the furring strips and the 2-by-4-inch studs. Measure and cut holes for electrical outlets, switches and lighting fixtures. Attach the drywall overhead to the bottom of the exposed flooring joists to form the bedroom ceiling.