Measure the height and width of the back wall of the TV opening. Cut a piece of drywall to fit this space. Install it by screwing it onto the wall studs using 1 1/2-inch drywall screws.
Measure the floor and ceiling of the TV opening. If these elements are square or rectangular, cut them and then install them. If they are unusually shaped, it may be easier to cut only the back edges, leaving the fronts large, screw them into place and then trim the front edges by running the utility knife along the front edge where it meets the wall. This guarantees an accurate cut.
Measure the side walls of the TV opening. Cut them to size and install them with drywall screws.
Fill in any gaps that exist between pieces of drywall that are joined at an angle with drywall compound. Scrape it smooth with a drywall knife so that it fills the gap but doesn't protrude past the faces of the boards. Allow the compound to dry completely.
Apply drywall tape onto all of the joints by spreading drywall compound thinly over the joints, embedding the tape in it and then applying another layer of drywall compound over the face of the tape. Smooth out the surface of the compound as much as possible to reduce sanding. Allow it to dry completely.
Sand the surface of the dried drywall compound smooth using 120-grit sandpaper and a sanding block.