At the end of the Hadean Eon and the beginning of the Archaean Eon, about 3.8 billion years ago, Earth was still about three times as hot as it is today, but it was no longer hot enough to boil water. Most of the Earth was covered with oceans, and Earth's atmosphere was mainly carbon dioxide with very little oxygen in it. Just a little bit of land was forming as volcanoes began to poke out of the water. Most of the rocks were igneous or metamorphic like granite or quartz. But the earliest sedimentary rocks like sandstone also formed, mainly in the oceans, during this time.
About this time - around the beginning of the Archaean Eon, about 3.8 billion years ago - the earliest living cells formed on Earth. These cells all lived in the oceans, which were probably much warmer and more acidic than they are now. By about 3.5 billion years ago, these early cells had evolved into simple prokaryote cells. For the rest of the Archaean Eon, there were only prokaryote cells on Earth (and the vast majority of cells on Earth are still prokaryotes).
By three billion years ago, some of these prokaryote cells evolved to be able to make their own food out of sunlight, water, and carbon dioxide. We call this process photosynthesis. Cells that got their energy by photosynthesis excreted (pooped out) oxygen, and once a lot of cells were photosynthesizing there began to be more and more oxygen on Earth. But during the Archaean Eon almost none of that oxygen was in the atmosphere - instead, iron and sulfur rocks mixed with early oxygen atoms to make rusty red rocks and limestone.
There were probably many large asteroids that hit the Earth during the Archaean Eon. These asteroids would have killed many small living creatures and may have encouraged others to evolve.
About 2.5 (two and a half) billion years ago, the Archaean Eon ended and the Proterozoic Eon began.
Bibliography and further reading about the Archaean era and geology: