1. My pet has a 'travel pillow'. We got a pillow that fit in his kennel, cut it open, and sewed a zipper on it. When we travel in hot weather, we just put a plastic-covered ice pack inside. My dog looks best groomed, so I always have him trimmed up before we travel. We live in a warm climate, so traveling to a cold one in winter can be quite a shock. To keep my dog from becoming a 'dogcicle', I invaded my nephew's leftover baby clothes. Depending on your dog size, kids' jogging suits (3-6 months works well for dogs under 15 lbs!) are warm, not too bulky, and comfortable. Just remember to cut a tail hole! For his little feet, I cut the fingers off an old pair of my dad's gloves and tucked the tops into the jogging suit cuff. I'm working on sewing them on.

2. When traveling by air with your dog/cat - PREPARE - contact the country where you will be traveling at least 3 months prior to find out rules governing that country. Ensure that you are able to meet these requirements and specifications. Pay attention to detail: ensure that your vet's full name and #'s are on each document and that they also add your pet's microchip type and #. 

3. When traveling with your dog or cat, it's a good idea to get an 'AVID' tag. These are special computer tags the size of the head of a straight pen that are inserted painlessly into the fatty area between the animal's shoulder blades. The law now requires that all animals that are 'found' by dog catchers, pounds, shelters, law enforcement etc., be scanned to see if they have an AVID tag. Once scanned, the animal's entire medical history, home and emergency contact numbers will show on a computer screen. I
had my e-mail address put on all of my animals AVID tags. It also helps identify WHICH animal is yours. This might sound lame, but say for instance that your yellow tabby cat has been missing for 2 weeks, has lost weight and become dirty, and now is in a cage with 42 other yellow tabby cats ... well you get the picture. AVIDs are not expensive at all. They are usually $10. They can be obtained at most veterinarian's and animal shelters. Some pet stores have AVIDs too. 

4. Before you plan on traveling with your pet in cold weather make sure the temperature is above 45 degrees F for flying. If the temperature is below, you will need to get a letter of acclamation from your vet saying what temperature your pet can withstand. If you are traveling overseas, you might want to plan ahead. Finding out the hard way is not fun. If the temperature is going to be low, and you are going to travel overseas, my advice is to leave your pet at a shelter or with family and friends until the weather warms up. You don't want to end up with your animal not surviving. 

5. When going on a trip with your dog make sure to have the following: 
Kennel 
Food and water bowls/food and water 
Short leash, long leash/extractable leash 
Info tag on collar 
Favorite toy and blanket 
Health certificate 
A sweater if traveling somewhere cold 
Grooming supplies: Brush, comb, shampoo, conditioner etc.. 
Pooper scooper 
Favorite treat 
Anything you think would make your dog more comfortable during the trip. 

6. If traveling by air take your dog out for a good exercise 30 minutes before you leave for the airport. When you get to the airport take your dog and let it go to the bathroom. If your dog is going in the cabin with you bring a few ice cubes in a bag and let the dog eat them every few hours. Bring a blanket of some sort to put over the bag (I think Sherpa is the best kind) when getting on and off the plane so the dog can't see out and get scared. If your dog is going in cargo and the flight is under 3 hours, put a bowl of frozen water in the kennel so the dog can drink it without worrying about it spilling. 

7. Cats like the same kind of music small children do. When taking my cats on trips play classical and other 'Lullaby' music so my cats fall asleep and aren't as scared from the trip.

8. When traveling by air, if the dog went in the cabin with you, as soon as you get off the plane (even before you get your bags) take your dog out for a walk. If your dog was in cargo, Get your dog before you claim your baggage and take it for a walk.
When you get to your destination, spend some time with your dog and get it adjusted to its new surroundings. Try to keep the same schedule as you would have at home.