Geologists theorize that liquid water has existed on earth from very early in geologic time.
Some of the oldest known rocks (>4 billion years old) were originally deposited as sediments in water. This means the rivers and oceans had to have existed at that time.
Originally, scientists thought the earth's water came from the earth itself, usually from volcanic eruptions (some water does come from these sources).
Recent work indicates that some (possibly most) of the water on earth may have arrived from extra-terrestrial sources in the form of comets (basically giant snockballs in space).
It is assumed that there were many more cometary impacts early in the earth's history, and that these led to the addition of massive amounts of water during the early stages of the earth's formation.
The overall volume of water on earth, while clearly not static in the long term, can be considered constant at human time scales.
However, the spatial distribution of water can and does change constantly, moving between numerous "temporary storage units."
This movement is called the Hydrologic Cycle
Several important ideas here:
Most of the water on earth is the same water that has been here since the earth first formed. However, the spatial distribution of water can and does change constantly, moving between numerous "temporary storage units."
These include the ocean (obviously the largest), glacial ice, groundwater, streams, lakes, the atmosphere, organic material, Pepsi cans, and many, many others.
The cycle has 4 main parts, and involves either a change of state or the interaction of water and gravity.
Evaporation: Phase change from liquid to vapor.
Condensation: Phase change from vapor to liquid.
Precipitation: Interaction of liquid and gravity.
Collection: Interaction of liquid and gravity.
The water is usually purified as it changes state.
This is a REAL GOOD THING, since we tend to mess it up, no matter what state it's in.