Does the amount of water on the planet earth remain consistent?

Yes. Until we start exporting water off-planet, the net amount of water on earth pretty much stays the same. It would take a long time to explain every way in which water is conserved, but water in water form doesn't go anywhere. Whether it is frozen, liquid, or gas, it stays right here on earth. Evaporated water condenses and rains again eventually.

Occasionally water in nature is used in different chemical processes that split the water molecule and use it up to make a new chemical, such as sugar. Most of these events have another event that takes those other chemicals and and has water as a product of the reaction. For instance, photosynthesis (plant energy storage) requires water to produce fruit. Then digestion and respiration are both processes that produce water as you use up that stored energy. It's all a cycle (or several different cycles), and the net amount of water remains pretty much the same--if we lose water, the hydrogen and oxygen are stored in something that will make water when it is used up.