Wash the pet in a combination of 1 quart of hydrogen peroxide, 1/4 cup baking soda and 1 teaspoon liquid dishwashing soap. Rinse the solution out of the pet's fur after several minutes, and wash the pet with pet shampoo. Discard the unused solution, and do not allow the solution to get into the pet's eyes.
Alternately, wet the pet's fur, and apply a solution of 2 parts water to 1 part apple cider vinegar. Work the vinegar solution into the pet's fur, and rinse after five minutes. Another option is to mix 1 cup of vanilla extract in a gallon of water, and work the solution into the pet's fur. Allow the mixture to remain on the pet's fur for 10 minutes then shampoo as usual.
If other options aren't available, pour tomato juice in a container that is large enough to bathe the pet, and set the pet in the tomato juice. Rub the juice into the fur, and allow the pet to remain in the tomato juice bath several minutes before rinsing and washing with pet shampoo. Wash the pet outdoors whenever possible to prevent spreading the skunk odor indoors, and rinse the pet's eyes with a commercial eyewash if necessary.