Find the wall studs near the bowed section with a stud finder. This helps you locate the seams of the bowed panel for easy removal. Mark this spot with a pencil.
Pry off the old drywall with a pry bar. Insert the end of the pry bar through the drywall on top of your pencil marks and pry out. This should pop the drywall off of its nails or screws. Continue until the entire section is removed.
Remove the nails or screws left behind in the wood studs. If the old panel was nailed, flip your hammer around and pry the nails out. Place them in a small bucket to keep them contained. If screws were used, reverse the direction of your cordless screwdriver and remove them.
Cut the new drywall to fit the area with a utility knife. Measure out the space that is now open. Make cut lines using these dimensions on the back of the drywall panel with a pencil. Score on top of the cut lines with a utility knife. Snap the drywall to break it. Cut through the paper with the utility knife.
Hang the drywall in place with a cordless screwdriver and drywall screws. Fit the new drywall panel into the empty space. Drive screws through the drywall into the wall studs. Use one screw for every 12 inches on the vertical. The screw heads should just dimple the paper of the drywall.
Tape the seams of the drywall patch with joint tape. Use self-adhesive tape to eliminate having to mud before applying the tape. Press down firmly to create a good seal.
Apply joint compound over the tape and the screw dimples with a drywall knife. The tape should be entirely covered with joint compound. Apply a 1/4-inch-thick coat over the tape and the dimple marks. Scrape off the excess compound with the edge of the drywall knife. Let the compound harden for four to six hours.
Sand the joint compound smooth with a fine-grit sanding block. The surface of the drywall panel should be smooth to the touch and level.