How do you stop cats from clawing?

I agree with the others that keeping their nails trimmed is a good start. If you don't feel comfortable, take them to the vets and have them show you what to do. Try to offer them any and all appropriate scatching items. Cardboard, pieces of carpet, some cats also love scratching a log or piece of wood, sisal rope scratchers. If you can figure out what texture they go for and work it into an appropriate scratcher it might solve your problem. Also try catnip on all of the above!

Bo is somewhat addicted to his scratch pad. I picked it up at Petco, or Petsmart - it's a jute mat with non-skid backing and a zipper to replace the catnip inside every now and again. Take it home, let the cat see/smell it, and give it a couple scrapes with your nails. They usually catch on pretty quick.

Also - if you're looking to do this on the (really) cheap - cats adore cardboard boxes. If you're feeling crafty about it (and don't want what looks like a kitty-hooverville in your livingroom) go to lifehacker.com and search "cardboard cat". Someone has put up instructions for a cardboard kitty chaise.

If they keep it up, there are some sprays you can purchase to discourage the cats from being anywhere near their favorite targets. Also, Petsmart/Petco sell what are called Softclaws. They're little caps you can buy to essentially glue on to their claws. You need to ask for them - they are apparently a high-theft item so they are kept off the shelves. Or you can order them online in tons of colors.

You could try using a squirt bottle full of water and spray them with it when they start to claw.

Do they have any furniture of their own they can claw? If not, try buying some cardboard scratch boxes, a scratch post, something. You can try sprinkling catnip on it to draw them to it and entice them to use it.

Also, trim your cat's nails will help a lot. Cats claw and scratch at objects to play, but they also do it to "sharpen" their claws, much like us humans clip our nails. Keeping their nails trimmed back will help immensely.

Like everyone else, I thoroughly endorse trimming nails. It's something you can wean them into the habit of (so that it is not a fight to do so), and it also helps for those times they just want to show you their appreciation of your affections. :)

Another thing I use is the scratching board - a corregated cardboard strip with catnip hidden in it. It's cheap ($3 - $5), biodegradable, and my cats love it. It really does help to take the attention from drapes and furniture.