The Earth was formed by the accretion of a large number of rocky planetesimals from the disk of material around the Sun. The energy of the impacts kept the early Earth molten, so heavier elements (iron and nickel primarily) sank to the core, while lighter elements (Mg and Si combined with O: rocks) floated to the top (and light gases made our atmosphere at the very top). The Earth is still has a large melted mantle inside; a thin crust (50-100 km) has solidified on top.  Heat is escaping (but slowly, since the surface to volume ratio is very small). It is convected from the inside to the outside by hot mantle rising, cooling near the surface, and then sinking (because cooler material is denser than hotter material). This motion gives rise to continental drift, in which the large tectonic plates are buffeted from below. In some places they collide and one is subducted under the other. In other places they pull apart and new crustal material appears from below (the mid-oceanic rift zones). It is this process which produces many earthquakes. We can learn about the interior structure of the Earth by measuring seismic waves produced by earthquakes; the waves travel through the Earth at different velocities depending on the temperature and density along the path. Pressure and shear waves also travel differently; no shear waves can pass through liquid (so we know we have a liquid outer core). The convective motions in the core combined with the Earth's rotation make a magnetic field around us which protects us from the solar wind.

The Earth's rotation axis is tilted with respect to its orbital plane, and acts like a gyroscope (pointing at the same star over long periods of time). This gives rise to our seasons, since sometimes a given pole is pointing more toward the Sun, and sometimes more away. Those times are the solstices; halfway between the tilt is perpendicular to the Earth-Sun line (and so irrelevant) - those are the equinoxes. Actually the Earth's pole slowly precesses (also like a gyroscope, uner the influence of the Sun's gravity), so the Pole Star today was not always so. The pole describes a slow circle in the sky with a radius of 23 degrees, taking more than 20000 years to make one cycle.

We have one Moon, whose composition resembles our mantle. Thus we think it originate from an impact of a Mars-sized body on the early Earth. We use radioisotope dating (decay of radioactive elements to more stable forms to date the age of rocks). This works by measuring the half-life of the unstable form: the amount of time it takes for half of an original amount to decay (so after 3 half-lives there would only be an eighth left, for example). The Moon is almost as old as the Earth (4.5 billion years old). We can tell that during the first half billion years there was a period of intense cratering (using dating of rocks brought back by the Apollo astronauts). This was the collection of debris left over from the formation of the planets.  The Earth experience similar cratering, but geology and erosion has erased the evidence. Some very large impacts penetrated its early crust, causing the extensive lava flows that we call the "maria".The cratering rate has declined ever since, and is comparitively very low today. Because the Moon is a smaller body, today it is essentially solidified. Relative dating of impact craters can be done by seeing which ones overlie older ones.

The phases of the Moon are caused by the position of the Moon relative to the Sun. When it is sunward, it is harder for us to see the lit side, when opposite the Sun we see the full lit side. The moon's orbit is tilted relative to the Earth's, so the Moon does not always come directly in line with the Sun. When it does, we get eclipses: a lunar eclipse if the Earth's shadow falls on the Moon, a solar eclipse if the Moon blocks the Sun. It happens to have the same angular size as the Sun now, but that is a temporary condition. The Earth and Moon raise tides on each other (causing our ocean tides). This is due to the fact that gravity will be stronger on the side of a body nearer to the other attracting body (the tidal effect falls off as the cube of the distance). In the Moon's case the tides have locked it with one face towards the Earth; in the Earth's case the Moon is slowing its rotation down (aiming for eventual lock). The Earth's rotational angular momentum is transferred to the Moon's orbit, causing it to spiral slowly away (this takes billions of years to complete).