You can be like the grandma who puts plastic over her furniture. At least temporarily, consider putting heavy plastic over the furniture to prevent the behavior — and prevent reupholstery.
Meanwhile, give your cat something that it can scratch. Either build your own scratching post with four-by-fours or purchase a “cat hotel.” If you decide to construct your own, purchase a piece of sample carpeting and turn it over to the nubby jute side. While cats don’t like walking on the back side of carpeting, scratching at it is another matter. Appealing cat trees have a sturdy base and have at least one horizontal branch.
Encourage the cat by playing with it and feeding it near the scratching post. Tuck some catnip at the base and on the tree. You may even want to teach it a lesson in Scratching 101. Take the cat’s paw and show it how to scratch the post. Sometimes feline see/feline do is effective. You may also try waving a toy in front of the scratching post. The cat goes for the toy and digs its claws into the post, then you praise the cat. In older cats, you may need to repeat this scenario several times a day for a week to 10 days before it catches on. (You can teach an older cat new tricks; it just takes longer.)
As the cat begins to use the post, remove that tacky looking plastic off your furniture. If you catch the cat in the act of daring to scratch at your furniture, either hide around a corner and blast a bicycle horn or take an empty soda can filled with four pennies and throw it at your cat. Please, don’t test your aim. The idea isn’t to hit your cat with the can. Your intent is the startle the cat, and to deliver the correction without the cat realizing that you’re responsible for it. Otherwise, the cat will simply scratch at your dining room table when you’re not looking. Then, the entire affair will become a cat and mouse game as you attempt to catch kitty in the act. It’s a game you will never win.