Purchase a cushion cover in the pattern that matches your current design. It may be difficult to find the exact pattern to use for the fabric on each cushion. You can either redo all three cushions in a new pattern that coordinates with the rest of the fabric on the couch, or contact the manufacturer to see if they have replacement cushions available in the same pattern.
Remove the damaged cushion from the couch, then unzip the back of it to remove the cover. You may need a different cushion for the middle of the couch than you will for the end cushions, since those cushions have sides sticking out in front of the arm on many sofa styles.
Leave the batting, which is the pillow-top layer that sits on the cushion, and the netting, which holds the batting in place, on the cushion. Slip the new cushion cover over the cushion. It may be a bit tight to get on, but start at the bottom and slide it slowly from each corner up until you can zip the cushion completely.