If at all possible, arrange in advance for a bedroom or other space to be set up for your pet, containing food, water, bedding, toys and perhaps some articles of furniture that the pet shows preference for. Make a sign warning people that pet(s) are within and stick it on the door so your pet doesn't get inadvertently released or forgotten. Check periodically to make sure that your pet is okay and that the temperature is not too hot or cold.
4. Take your pet on a tour
Allow your pet to thoroughly inspect its new home. Go with it if possible, if it is too young or behaviorally challenged at this point to be trusted alone. Once your pet has made the rounds in the house and outside (especially for dogs), it will feel better about this new property as its home.
5. Re-establish a routine ASAP
Your pet's regular schedule of walks, feeding, grooming, etc. should be instituted as soon as possible. A regular schedule will make your pet feel more secure in its new home.
6. Keep your pet under control
While it is wise to always keep all kinds of pets confined when you can't supervise them, if you are in the habit of allowing your cats outdoors, hold off for a week at least so that they have the chance to bond with their new home. Never let your pets roam far afield; it is not only dangerous for them, it is also inconsiderate of your neighbors to allow your dog or cat to run hither and yon over their property. M Shane