We have "owned" cats for a grand total of about 8 weeks now, so I'm not an expert on cats, but I do seem to have fixed this problem.

We use a child's water pistol to discourage the cats from doing things we don't want them to do (which basically comes down to scratching furniture/carpets and taking food from the table). I expect some people might object to the water pistol, but it works for us. After a few shots you don't end up squirting them anyway, because as soon as they see you pick it up they realise what might be coming next.

There is an arm of a sofa that one of our cats persists on trying to scratch. We find if we leave a through over that arm she won't try. As soon as we remove the throw she tries to scratch the sofa. We can live with that. She also still scratches the carpet sometimes, we are working on that.

We also have plenty of things for them to scratch. I made a big chunky scratching post (which they rarely use of course) and we also let them scratch all the door mats in the house (big coir and sea grass ones). Max likes the door mats, Cookie must do most of her scratching outside now (some of our trees have lots of scratches on their bark now).