The cartesian diver is quite easy to make and operate. The only materials required are an empty plastic bottle (such as a two liter soda bottle) and an eye dropper + ordinary water. The construction directions are easy to carry out.
For some added amusement you can make a hook with your eye dropper and put something heavy at the bottom of the bottle with a loop. Then the game is to hook your diver at the bottom.
Why does it work?
The key concept we need to consider is bouyancy. Would a glass rod float in the water? NO, it doesn't float because the glass is more dense than the water is (a small glass marble wouldn't float either - so it is not just the mass (weight) it is the density - how much mass (weight) for a given volume.) The air inside the eye dropper, however, is less dense than the water. When you first put the eye dropper in the water there is a large enough volume of air inside it that it floats.
What happens when you squeeze the full bottle? You apply pressure and inside the bottle the pressure increases (you might experience an increase in water pressure when you dive to the bottom of a deep pool.) The increase in pressure causes the volume of the gas inside the dropper to decrease. If you look closely you can see the water go up into the dropper bottle. Now, with a smaller volume of air in the dropper it is more dense than the water and it drops to the bottom of the bottle. When you release the bottle, the pressure returns to its original value, the air in the dropper fills it once again because it's volume increases, and the dropper floats to the top.
Some Links
Top diver - a modification of our demonstration
Exploratorium - Their version uses a condiment package
Buy a diver - yep - if you don't want to make one you can buy one on the web.
Bottle fun - lots of experiments you can do with 2 liter bottles.