If Possible, Move the Pets Separately
Ideally, you should move your pets to your new house the day before the big move so they have a chance to get acclimated to the new environment. This will let you focus on getting the truck loaded and cleaning up, rather than worrying about a wining cat or dog. Of course, this may not work for your schedule, but it will make for a much better experience across the board.
Create a Quiet Environment
Your pet is going to have to ride in your car or in the moving van on the way to the new house. This will require you to put him in a carrier or kennel, unless you have a dog that will stay calm in the car. For most pets (dogs, cats, or otherwise), it would be best to create a quiet environment during the drive. This is especially true if you are going on a long trip. Play some soothing music, and consider putting a blanket over the cage to minimize lights and sounds. This should keep the pets calm for the drive.
Make Yourself Visible at All Times
Try to position your pet so that he can still see you in the car. Pets like to see someone familiar when they are going to an unfamiliar case. Most dogs will happily look out the window, but some will shy away in the car. Cats and other pets tend to have a problem in vehicles, so they need to see you more than your dog. Having you around will make an otherwise scary ride seem less scary in the long run.
Let Your Pet Explore the New House
Before you start moving in all of your furniture, give your pet a moment to look around the new place. This will give him a chance to get familiar with the surroundings and feel more at home. If you have fish or rodents, you might just want to put them in a quiet closet until the commotion is complete. Then you can bring them out and let them see everything when no one else is in the home. For cats, consider putting them in the room where their litter box will be so they get used to the area before going on an adventure.
Above all else, try to stay calm when you move. Your pets will feed off your energy – good or bad. Think about your pet's needs as you transition to a new home, any they will be happy in no time.