Remove all of the floor coverings in the room. Also remove any nails or carpet tack strips. Sweep the room thoroughly to remove dust, dirt and debris.
Remove the vertical pieces of plywood or boards that border the sunken area with a crowbar.
Measure the height from the sunken area's subfloor to the top of the upper area's subfloor. Also measure the exposed joists and the height of the subfloor in the upper area. Generally, these are 2-by-6 boards and 3/4- or 1-inch plywood.
Measure the length and width of the sunken area. Add 2 feet to the measurements.
Check the subfloor in the sunken area. If it is cement, tape a 6 mil plastic vapor barrier over the cement, extending it as far as possible under the existing joists.
Measure the space between the bottom of the joist and the subfloor. Lay a board every 24 inches across the lower subfloor, perpendicular to the joists. For example, if the space is 1 1/2 inches tall, insert pressure-treated 2-by-4 boards to help support the new joists. Nail through the 2-by-4 boards at a 30-degree angle into the subfloor.
Cut the new 2-by-6 floor joists 2 feet longer than the sunken area. Slide the first board 12 inches under the original raised floor, butting it up against the subfloor and floor joists. Check with a spirit level to ensure that the new joist is perfectly horizontal. While a helper holds the board in place, predrill four 1/4-inch holes through the existing joist and 2-by-6 board. Insert the lag bolts, tightening the nuts with a wrench or socket set. Repeat at the opposite end of the board.
Attach a new floor joist at each of the old joists, spanning the sunken floor. Nail the joists to the 2-by-4s underneath, again nailing at a 30-degree angle on both sides of the joist.
Measure and cut 2-by-6 blocks to fit between the new joists. Insert a block above every 2-by-4 support. Hammer the nails through the block and into the joists at a 30-degree angle.
Measure and cut 4-by-8-foot sheets of plywood to fit onto the new joists and blocking. Draw a bead of construction glue on top of the joists. Place each sheet of plywood in place, tapping the tongue into the groove of the previous sheet. Cut the tongue off the last sheet of plywood so it fits perfectly into the space between the old and the new subfloor. Screw the plywood to the joists using deck screws every 6 to 8 inches.
Install your choice of carpet, tile, laminate or hardwood flooring.