Many people stress when they have to move house with their pets, especially cats as they are notorious for trying to get back to the old residence, so a little advice can go a long way.
Ideally, you need to keep your cat indoors for at least six weeks. To begin with, choose a room in the house that the cat can stay in with all toys, food, water, litterbox and bed, and that would become the cat’s safe place. Before the move, place a piece of clothing or cloth in the room that has both your scent and that of your cat on it, and just leave it in the room. If you can lay your hands on a cat pheromone such as Feliway, spray that around the room the day before the move, or at least prior to introducing the cat to the room. Humans cannot smell the pheromones and it won’t mark walls or fabrics, but it will be very calming for your cat.
Your cat should stay in this room for at least a week, possibly longer depending on the cat. Pay special attention to how well he/she is settling in. Obviously, you will need to visit him or her regularly in the room for play time, etc - the cat is not in prison. When you decide that the cat is settled enough in that room, you can open up another section of the house to him/her, just spraying a bit of pheromone to the new area - this lasts for about a month so no need to re-do the safe room.
If you have a large house, you should let the cat explore a bit at a time, and when he or she has become comfortable with the new area, another room can be made available, until the whole house has been explored and the cat seems calm and comfortable in the new surroundings. Moving into something smaller is, of course, a much easier transition for the cat.
When you let your cat outside for the first time, ideally you should be present just to keep an eye on things. Make sure that the cat is fed when it comes back inside at night around the same time - this will help it learn that this is home and where food is provided. This would also be the ideal opportunity to turn your cat into an indoor cat as it would have been living inside for several weeks already.
Generally speaking, with a bit of forethought and planning, moving house can be a smooth exercise for your cat.