Take the cushions and/or pillows off the sofa and set them aside. Move the sofa away from the wall into the center of the room, where there is room to work.
Turn the sofa over, putting the seat against the floor, exposing the underside of the furniture.
Pull off the mesh cover concealing the wooden frame by pulling out the staples tacked into the frame with a staple puller.
Locate the break in the wooden frame. In addition, look for stress marks or areas where the wood is slightly cracked and/or distressed. These will likely break in the future, and now is the time to address the problem.
Squeeze glue onto both sides of the break in the frame. Push or pull both sides together and set clamps around the break to hold each side in place as the glue dries overnight.
Remove the clamps once the glue has dried. Situate spiked wood joiners on the sides and top of the break and gently tap the joiner into the frame with a hammer. Also hammer wood joiners into the sides and top over any stress marks or cracks to prevent breakage in the future.
Stretch the mesh cover back over the wood frame and staple into place. Turn the sofa back over and replace the cushions.