Remove the visible staples near the sagging section of the couch with a staple puller. Flip the couch upside down, if necessary, to access the staples on the bottom of the couch but only remove the ones that will help you get access to the sagging portion. Continue to remove staples until the sagging area is partially exposed.
Use a seam ripper, if necessary, to pull apart any seams that prevent you from gaining access to the sagging area. Rip only the minimal amount of seam necessary to work on the sagging portion as this seam will have to be reattached in an unobtrusive manner.
Cut the fabric with a pair of scissors or a utility knife if the staple removal and seam ripping do not provide sufficient access to the sagging section or you will be recovering the entire couch anyway. Keep the cuts smooth and as discreet as possible to facilitate an easy reattachment of the fabric.
Slide plastic pieces that are 1/4-inch in thickness or more over the sagging section of the couch underneath any existing support cushions. Try to make the plastic pieces span the wood frame of the couch, working diagonally in the corners if they are not long enough to cover it horizontally. Add as many sections as possible until the couch cushion appears firm and raised.
Add 1/4-inch-thick wood boards instead of plastic if the sagging is significant or if the weight on the couch is very high. Position them across the frame then screw them to the frame with 1-inch wood screws for additional stability, particularly for couches that bear heavy loads.
Add extra stuffing over the supporting plastic or wood to provide further padding to the hard supports. Pull the fabric of the couch back into place. Staple it as discreetly as possible into the cracks of the couch and underneath it with a carpentry stapler. Some stapling can be done on the rear of the couch, if necessary, as most couches are positioned against the wall, and the staples will not be seen.