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The universe expanded from an infinitely hot and dense point
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A supernova that happened nearby caused the dust cloud to increase its rate of spin, creating lumps of matter. These lumps crashed into each other to create various planets and stars, including Earth.
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The most widely accepted theory is that there was a large meteor that hit the earth and caused chunks of it to fly off, forming the Moon.
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After a period of rest, the earth cooled down enough that water could be in a liquid state.
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During this time, asteroids and failed planets began to stop falling down and hitting the earth.
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The current understanding is that the inner core was formed around 1.5 billion years ago, and will continue to exist for more than a billion years. However, it is not proven that the inner core exists, and most of the "facts" are theories yet to be proven.