Measure across the ceiling by running your tape measure from one corner and across as many joists as possible to the point nearest 96 inches. Move back along your tape measure to the center of the nearest joist and take note of the measurement at that point.
Place a 96 inch board flat on your chop saw. Measure along the board to find your ceiling measurement. Hold the board firmly against the guide of the saw and lower the saw arm without pulling the trigger. Move the board along the saw to line up the blade with your mark. Pull the trigger and cut the board at the pencil mark.
Attach the board to the ceiling with the Phillips bit on your drill using the 3 inch drywall screws. Run a screw through the board and into every joist in the ceiling. Continue attaching boards while making sure that every board ends in the middle of a joist unless it meets a corner of the room. Place a row of boards every 2 feet across the ceiling parallel to the first line. Place your last row of boards against the far wall of the room.
Cover the boards with plywood. Run 1 inch screws through the plywood and into your boards every 8 inches along each row of boards. Measure any cut pieces and use your 'T' square as a straight edge when drawing your cut lines. Cut the plywood with your jig saw by following each cut line. Drill a hole with your 1/2 inch bit and cut out necessary sections with your jigsaw for lights and vents in the ceiling.
Remove existing lights and vents from the joists with your screwdriver. Attach the fixtures to the outer face of your new plywood ceiling with their original hardware.