When moving, your cat should be the last thing you "pack up", if you're moving across town you should already have all the furniture in place including their cat condos, toys, litter box etc. before he arrives. If you're moving farther, be sure to transport your cat in a roomy carrier that's tall enough for them to stand up and turn around in. It will also help if you put something with a familiar smell in such as a towel from their basket. If your cat will be in the car for several hours, a litter box, food, and water will be essential. Also be sure to look for pet friendly hotels where you can bring your cat if you need to stop.
If you are still re arranging furniture when you arrive to your new house or if the movers are coming in and out, be sure to put your cat in a quiet safe room out of traffic and keep the door closed. Be sure to check on him periodically and pay extra attention to him. Make sure he has the necessities at all times such as their litter box, food, waters, and their cat condo or house to sleep in.
Make sure there is no way your cat can get outside. Even if your cat is an outside cat, they may still try to get back to their old home. After you've settled in make sure your cat is perfectly comfortable in their new house which might take several days, before you open the door for him.
Depending on your cat's personality, they will either be comfortable with exploring the whole house all at once, or they'll head straight for the room you're in or a hiding place and then venture out very slowly. This varies from cat to cat but no matter what be very patient with your cat and allow them to explore on their own.
Once you get all your furniture in place the smells will become familiar to your cat and they'll adjust real quickly. Remember this is a stressful time for you cat so be sure to pet and talk to them frequently and reinforce that this is a "good thing" and not a punishment. Even go as far to take your cat on a "tour" of the house in your arms so you can show him what's happening.