My pet sometimes scratches my cozy chair. How can I stop my pet from doing this?

Well ever time your cat tries to scratch at your cosy chair you say - "psssssssssssst -psssssssssssst - -psssssssssssst" in a firm voice. Thats how I learned my cat to stop scratching at my chair (it wasn't really a cosy chair because it had a broken spring but it still worked). Cheers!

make sure to provide 
a place for them to scratch somewhere.
I have a couple of big cardboard scratch pads 
taped together

I will assume your pet is a cat from the picture you put on here.
There are a few ways to do it. You can buy a can to spray on the chair; this can has a smell that cats don't like.
Another way is firmly tape something to the area where the scratching is happening. Try: aluminum foil, or a plastic bag. It must be taped firmnly so your cat can't take it off. How this works is your cat won't like the feel of these things on his/her paws.

You can get nail clippers for cats and trim the nails. Or if you can't do it, take it to a groomer and they will do it.