To keep your cat from shedding, just give the little beggar a good coat of varnish.
In all honesty:
Generally, when you use formal flatware, use the forks and spoons furthest from the plate first and work your way in. Exception: The salad fork is usually closest to the plate.
Dirty utensils cannot touch the surface of the table or the tablecloth, ever. Even the handles of everything should not touch the table.
When you're finished, set your used utensil down on a plate crossed over one another or horizontally across the plate with the knife blade toward you so the waiter knows you are done. Do not leave anything in a bowl or cup (that’s why there’s usually a flat dish under the soup bowl people!) where it might flip and assault your host or other diners.
Between bites, your utensils should rest on the edge of your plate. Your knife on the back of the plate, fork on the side of the plate.
Your napkin goes in your lap. You are not actually supposed to get in dirty either. You are supposed to clean your mouth with it, but you just dab discreetly at your mouth.
Do NOT lean over the table. Bring your food up to your mouth without leaning forward.
Sip your soup from the side of the spoon after diping it in the soup away from you and wiping the bottom on the edge of the bowl. You never put the whole spoon in your mouth. You eat the crackers by taking a bite of the cracker while you eat the soup, you do not crumble crackers into your soup.
Ice cream is eaten by turning the spoon over and licking the concave side (that is why the spoon is shaped that way, to fit your tongue).
You eat bread by tearing off a piece and placing the rest on your plate. You butter that piece in your hand, set the knife down, then eat that piece. Repeat.