Travels with (or without) Fido; Protecting Your Pets (at home or away), by Hal Gieseking. Illustrated by Dick Kline.Stockbridge, Massachusetts: Berkshire Traveller Press. $3.95.

Closing your front door in the face of your faithful dog or cat -- to whom you can't explain that you will be back from your trip up the Amazon in a mere 41 days -- may be the most agonizing part of travel. To cope with this problem, Hal Gieseking, consumer editor of Travel/Holiday magazine and author of "The Complete Traveler's Handbook," soon to be published by Simon & Schuster, has written a book describing ways to lessen the unpleasantness for both pet owner and pet.This whimsical, very specific, and practical volume includes suggestions for obtaining and briefing the pet sitter (what furniture pet is allowed on, name and address pet of store carrying Yummy cat food, etc.); how to measure pet for the right size of kennel for shipment by air; how to acclimatize pet from kitten or puppyhood to the car; and how to pick a pet carrier for the car (big enough for the animal to turn around in -- unless it's grayhound; "they turn into whirling dervishes," Mr. Gieseking says; "it's a strange characteristic of the breed").

There are also instructions for training your dog not to destroy the furniture when you leave him alone.

The six suggestions for coping with a lost pet -- whether it is lost on the road or in your own neighborhood -- are alone worth price of the book. "In the majority of cases the pet is not found," Mr. Gieseking says. "But you can double your chances of getting your pet back if you remember that, unless the pet has been injured or stolen, most pets do not wander more than a mile and a half from home. The most effective technique is to do a flyer on your pet -- offering a reward without mentioning the amount or animal's name -- then go to any direct-mailing house in your city and do an area mailing. Then everybody in your ZIP code will receive a description of your lost pet.

"Also take an ad in the paper, again offering a 'large reward' without specifying the sum. Petnappers read the papers for ads like this, figuring that the rightful owner will pay more than anyone else.

"It's important to take all these steps," Mr. Gieseking says, "because you have the feeling that you've done everything you can. . . . Then you can't reproach yourself afterward."

But "Protecting Your Pets" also copes with problems around the house. "People think they just instinctively know how to care for their pets and that's not necessarily true," says the author, himself the owner of a sprightly West Highland terrier named Danny.

An example: "Most people who are going away for the day will simply put the pet in the basement. The danger is particularly acute with puppies, as this is a stage where they are exploring the world orally -- they will chew or bite on anything. It's fine to leave your dog in these areas, as long as you've made sure that there are no dangerous substances -- soaked in a household cleaner, for instance -- within puppy- reach."

Mr. Gieseking says that Danny doesn't like to travel a great deal. "I'm still working on his training. But he always rides in the back -- that's another major mistake that people who love pets often make: letting their pets ride in the car next to them. There's always the danger that the pet may bolt from the car and run away. The other problem is that the pet may see something on the driver's side and lunge over you. Dogs and cats have been the cause of accidents on the road."

Mr. Gieseking especially warns against against leaving any animal -- short-nosed dogs are particularly vulnerable -- in a close car on a warm day, even for a few minutes. A suggestion I liked: giving your pet ice cubes to lick on during a long, hot car trip.

"Protecting Your Pets" is not available in all bookstores. If you can't find it in yours it may be obtained by sending to: Gieseking & Clive, Inc., PO Box 716, Bronxville, NY 10708 (send $3.95 plus 75 cents postage and handling).