Measure the distance between the standard ceiling and the recessed ceiling with a measuring tape. Measure the width and depth of the recessed ceiling area.
Cut two sections of 1/2-inch-thick drywall equal to the width of the recessed ceiling and the distance between the standard and recessed ceiling with a drywall saw. Cut two additional sections equal to the distance between the standard and recessed ceiling and 1 inch shorter than the depth of the recessed ceiling.
Place one of the width sections against the studs between the standard and recessed ceiling areas. Use an electric screwdriver to attach the drywall to the studs with 3-inch drywall screws. Repeat this process with the remaining width section on the opposite side of the recessed ceiling.
Install one of the depth sections by attaching it to the studs with 3-inch drywall screws. Repeat this process with the remaining depth section at the opposite end of the recessed ceiling.
Cover the edges and seams of the drywall with drywall tape. Apply drywall compound to the tape and screw heads with a 3-inch putty knife. Allow the compound to dry for at least eight hours.
Sand the drywall surface with a palm sander to smooth out the compound.