Make sure your pet is wearing proper identification like collars and tags. You may also have a micro-chipped implanted that stores your contact information.
Keep your pet's documentation with you and in a safe place. This includes current vaccination records as well as documentation on tattoo numbers, microchip numbers, license numbers, spay/neuter certificate, phone number for your current vet, and a recent photo of your pet.
Consult your vet to ensure your pet is in good health for traveling. Your vet may also be able to provide other information relevant to moving with your pet to a new city or town.
Keep your pet properly secured while the movers are packing/transporting items. Regardless of how well-adjusted they may be, your pet may get "spooked" or "startled" by all the noise and activity -- and you may be too busy to notice him bolting out the door or the yard.
Keep your pet with you at all times, in a secure kennel or crate; or place them in a room that's "off-limits" (make sure you tell everyone, especially the movers); or have a trusted family member or friend watch your pet off-site while you manage the moving crew.
Pack a bag for your pet. Include bedding, towels, toys, treats, food & water (eating the same food will help your pet avoid an upset tummy), bowls, leashes or harnesses, kennel or crate, plus any medications your pet requires. A pet first-aid kit is also a good idea.
Take your pet with you in the car, if at all possible. Your pet will be safer and more comfortable with you than being transported by strangers. You'll feel more secure, too, knowing that your pet is secure with you.
Get your pet accustomed to car travel. Take short trips at first, then gradually increase the time. If your pet just doesn't seem comfortable, consult with your vet who may be able to offer suggestions.
A travel kennel, crate, or doggie seat-belt is a good idea to help keep your pets safe. Do not transport them in the open back of a pickup truck, and do not permit them to ride in the front of the car or bounce around wildly in excitement. These things can distract the driver from paying proper attention to the road.
If you must transport your pet by air, give yourself ample time to research airline regulations. Consult with your vet, too, and take precautions to help ensure your pet's safety.
Make advance accommodation arrangements for any overnight stops along the way to your new home. When traveling with a pet it's always best to call ahead and book pet-friendly lodgings to ensure you both have a place to stay for the night.
Once you know your new address, remember to get updated tags as soon as you can. Many pet stores now have automated tag-making machines where you can quickly create a new tag.
Research pet regulations (such as health regulations or quarantines, or required documentation) for your new home city or town. This is especially important if you are moving across international borders.