How does the amount of water on the earth change over time?

The amount of water on the Earth doesn't change very much at all. Trace quantities are dissociated into hydrogen and oxygen by sunlight, or launched into space on our various space craft. Water hardly ever arrives on the Earth from space, but a medium sized comet could deliver billions of gallons of water (and knock our civilization into a new Dark Age) if it collided with the Earth.

Many scientists believe that cometary impacts may have provided the majority of Earth's water when our planet was still young.