Remove the cushions from the couch and examine the straps underneath. The straps typically wrap over the frame and attach to the bottom of the frame. Turn the couch upside down to reach the staples. Push the edge of a pair of needle-nose pliers under each staple and wiggle the staple until it comes loose.
Peel the broken or damaged strap away from the couch. Remove the staples on the other side of the frame, which keeps the strap firmly affixed to the couch. Examine the couch for any other broken or damaged straps and remove those in the same way.
Unroll the new strap and place it on the couch frame. Wrap the edge of the strap under the frame and turn the couch upside down. Attach the strap to the frame with staples from a staple gun. Pull the strap over the couch frame and wrap over the frame.
Secure the opposite end of the strap to the couch with the staple gun. The staples go through the strap and deep into the wood, which keeps the strap in place. Trim off any excess material with a utility knife.
Repeat steps 2 and 3 for each broken or damaged strap on the couch. Danish couches feature dozens of straps moving horizontally and vertically over the frame for maximum support. Even a single damaged strap weakens the support.
Turn the couch back over and arrange the cushions on top. Sit on the cushions and move around slightly, ensuring that the couch does not sag. If the couch sags, remove the cushions and examine the straps for any weak spots. Remove the straps and replace with new pieces.