The first thing you should do is measure the size of your appliances to see if they will fit through the door. In some cases, you may need to remove the door to get clearance or bring the appliance in through a larger frame such as a sliding glass door. Once you have the dimensions and planned out the move, you can proceed to preparing the space and the appliances for the task.
Don't forget to clean the floors before moving heavy appliances. Dirt, grit, small rocks, or other foreign objects can damage your floors more than the appliances themselves. Vacuum, sweep, or mop the area around and under your appliance, as well as where you'll be moving the appliance.
Once there are no foreign objects in the area, you can put down a protective covering where you will be moving the appliances.
While you can use cardboard to protect a clean floor, it is the least effective way. Cardboard has a tendency to move and create friction on the floor as you walk on it which can create tiny scratches, especially in hardwood.
A much better way to protect your floor is to use leftover carpet pieces or runners. For the best protection, invest in some temporary flooring. When used properly on a cleaned floor, these methods will mitigate any potential for damage.