This illusion is so easy, and so good that you may have trouble believing your own eyes, much less making someone else believe that it is a simple illusion, and not a more complicated trick.
You will need two similar coins. You can use two pennies, two nickels, etc.
Stack one coin on top of the other and hold them between your index finger and thumb. Now rub your finger and thumb back and forth to cause the coins to slide back and forth across each other. When you look at it while the coins are in motion, you will swear that there are three coins.
This illusion is caused by persistence of vision. Have you ever thought about how your eyes work? Light hits sensitive cells called rods and cones, causing them to release chemicals. Those chemicals stimulate nerves, sending a signal to your brain. Those chemicals do not instantly vanish. For a very brief instant, they continue to stimulate the nerves in your retina.
Persistence of vision is what lets you watch a movie, which is really a series of still pictures. The pictures flash by very quickly, and persistence of vision lets your brain blur them together to make you think you are seeing smooth motion instead.
As you move the top coin to the end of its path in one direction, it pauses for a second, and then you reverse direction. Your eye continues to register the image for a fraction of a second after the coin starts moving in the other direction. Before the image can fade, the bottom coin has moved into the same position and the image continues. You see one coin against your finger tip, one coin against your thumb and a third coin, whose image is made up of the combined afterimages of both top and bottom coin.
For an interesting variation, use a nickel and a penny. The "third" coin will seem to be the same as the top coin when viewed from the top and the same as the bottom coin when viewed from the bottom.