Pet stores are full of complicated dietary supplements for dogs and cats, but one of the best is flaxseed oil. I use it for my pets every day as a supplement to their food.
The seeds of the flax plant (Linum usitatissimum) contain alpha-linolenic acid. This is a vegetable-based fatty acid that does wonders in keeping an animal's coat in top condition and cutting down on shedding.
What I find interesting about using flaxseed oil for pets is that it has been used for at least 100 years. I have dog books dating back to the early 1900s that say it is beneficial to strain your dog's drinking water through flaxseed to improve the condition of its coat.
In the original "Lassie Come Home" movie of 1943, the character played by then-child star Elizabeth Taylor suggests this to Lassie's new owners, as they are looking at the poor condition of Lassie's fur.
You can buy pure flaxseed oil at any health food store, and all you need to do is add it to your pet's food every day at the rate of one teaspoon for every 10 pounds of its body weight.