How do the relative positions of Earth, the moon, and sun cause the phases, tides, and eclipses, and determine time on Earth?
Moon phases are what of the moon we can see from Earth.
Lunar tides are caused by the moon's gravity pulling on the water on Earth. High tide occurs when the moon is directly in line with the body of water in question. Low tide occurs when the body is perpendicular to the force of gravity.
Solar tides are caused the same way as lunar tides, except that the sun's gravity is pulling the water and that they don't tend to be as powerful.
However, when combined with lunar tides, they can create what are known as spring tides, which can be either extremely high tides or extremely low tides. There are also neap tides, which are the opposite of spring tides.
Lunar eclipses are caused by the shadow of the Earth as it passes in between the sun and the moon. The moon can look red because of the sunlight passing through Earth's atmosphere before reaching the moon.
Solar eclipses are caused by the moon passing between the Earth and the sun. Because of the distance between the two, the moon can block out most of the sun, except for a "halo" surrounding it.
These positions determine time on Earth because they're constant.
For example, one rotation of the Earth takes 24 hours, one revolution around the sun takes 365.25 days, etc. This makes it very easy to create a standard system because no matter where you are in the world, this information stays the same.