Measure the basement dimensions and draw a plan for installation of electrical outlets, switches and light fixtures. Locate existing HVAC ducts and draw a plan for connecting new vents for the basement space.
Check the basement for signs of cracking concrete or water leaks. Patch cracks with new concrete and paint the walls and floor with waterproofing paint.
Glue insulation boards to the walls and spaces between ceiling joists with construction adhesive. Cover the insulation boards with plastic vapor barrier and seal the seams with duct tape.
Install HVAC vents in the ceiling and connect them to existing ductwork with flexible ducting. Seal the seams with duct tape.
Frame walls around the edges of the basement approximately 1/2-inch from the insulation boards, using 2-by-4-inch lumber. Install base plates and ceiling plates and fill in the spaces with wall joists spaced 16 inches apart. Build frames around exposed HVAC ductwork as needed.
Hire an electrician to run power from the breaker box to the basement. Install boxes for electrical outlets and light fixtures and connect wiring -- make sure that the boxes extend 1/2 inch beyond framing elements to allow for drywall installation.
Cover wall framing and HVAC soffit framing with drywall boards nailed to the frame. Cut openings for electrical outlet, switch and light boxes. Seal and finish the joints with drywall compound and tape.
Install vinyl flooring to provide a low-maintenance, flood-resistance floor covering. Cut the flooring to size, roll it up and apply adhesive in small sections as you roll and press the flooring into place.
Paint the walls of the basement and install electrical outlets, light fixtures, switches, outlet covers and HVAC vent covers.