Turn the couch onto its back and unscrew the old legs. Replace them with new, higher legs by screwing them in where the old ones were. New legs are available in various sizes and styles, and the can give the couch a new, modern look. Choose legs that suit the room's existing decor.
Lift the couch and slide couch mounts under each leg or at all four corners. These are specially designed, commercially available mounts. They hold a lot of weigh and serve to raise beds or couches. Ensure each mount is evenly under each corner so the couch is stable.
Set the couch up on blocks. Use cinder blocks or blocks of wood. This is the most affordable method, often applied by students. Add a long couch cover to the hide the blocks if you desired.