The Archaean eon has began roughly 4600 MYA. Before this time, there was no Earth, no planets, and no solar system - just a lot of dust swirling in space around the primitive Sun; in time, under gravity, this dust formed planets, which included the Earth.
For first few hundred million years Earth was uninhabitable - bombarded by meteorites, poisonous gases and so. No life forms could exist on this planet.
4 billion years ago another planet may have slammed into Eath. According this theory, this impact broke away a piece of the planet, forming the Moon. This stabilized Earth's orbit around the Sun and created tides, which aerated Earth's first shallow oceans of first water - and life began to evolve.
The first signs of life date 3850 MYA deposits in Greenland. Nobody sure from where life came from, possibly from underground hot springs, which even now found containing and sustaining various species of animals.
For hundreds of millions of years, life on Earth was only bacteria that lived on ancient sea beds. Eventually they included cyanobacteria, which could photosynthesize energy from sunlight. From then on (around 3500 MYA) bacteria would be the dominant life form on ancient Earth.
The Archaean eon ended 2500 MYA, when the Proterozoic eon had began.