We wouldn't be human beings is we didn't wonder how everything began. There are, of course, many religious explanations for where it all came from; science tends to shy away from these not because scientists are non-religious, but because those supernatural explanations can really be tested in any way, while scientific explanations can be. Scientists also aren't that interested in a concept called panspermia: this is the idea that the earliest life began someplace other than Earth and was somehow carried here. Also not very testable (although some researchers believe that viable bacteria have been found sealed in meteors). We can't travel backward in time, but we can make predictions based upon hypotheses and test the predictions.
When scientists first began to think about how Life on Earth began, they looked at how Life worked around them, and everything depended upon fuel from plants to exist. The process of photosynthesis is very complex, and its appearance as a first step would have required some sort of supernatural intervention: this was known as the photosynthesis or plant problem.
It took better knowledge of how the Earth formed, and the chemistry of the early Earth, to solve that problem. The space dust that would have been coalesced to form the Earth, it turns out, has a decent proportion of organic molecules already in it. What emerged from that discovery was the Heterotroph Hypothesis, based on the idea of a Primordial Soup, a planet-covering solution of simple organic molecules, exposed to many types of energy, from lava heat to ultra-violet light to lightning in an extremely active atmosphere (it's still pretty active today, with an estimated 100 bolts per second planet-wide). The question was, could small organics, given such conditions, form larger organic molecules, and larger yet, until they became cooperative systems, able to self-organize, reproduce, and evolve? This is still an open question, but many small predictions based upon the hypothesis have been confirmed.
Some discoveries: RNA was found to have enzyme properties, providing a first possible living-system molecule that could have led to protein chemistry and DNA coding; some components of stardust were found to be lipids, critical in the formation of cell-like membranes; hydrothermal vents, with a fairly stable supply of raw materials and energy, and ecosystems based upon relatively simple chemosynthesis, were found; a primitive form of photosynthesis was found in bacteria near hydrothermal vents; a layer of rust in the fossil record indicated a rough date for the appearance of widespread release of oxygen from photosynthesis, after indications that life already had existed for some time; chemistry very much like the hypothesized primordial soup can be found elsewhere in the solar system, such as the moons of Jupiter and Saturn.
Unless we find a world in the early stages of developing its own living systems (which might be happening deep in those moons), we can't be too sure that it works the way the hypothesis says, but the evidence slowly mounts.
A broad assortment of creation stories.
More on panspermia.
Primordial Soup ingredients found on comet.
Scientists repeat one of the first experiments about the first primordial chemistry.
How'd it get to be RNA?
"Soup" from volcano.
More on that primitive photosynthesis.
And could conditions found on other planets or moons produce a type of Life?
The basic processes of life were first developed in prokaryotes - they were the first photosynthesizers, the first aerobes. They spread across the globe, but they were limited. Prokaryotes can be found in simple colonies, and different species can work cooperatively together, but they can't do the complex jobs that eukaryotes can. Particularly, they can't form multicellular systems.
It's unclear when eukaryotes, with their specialized chambers, evolved, or when they added to those chambers by taking in specialized prokaryotes and using them (the endosymbiont theory), but most evidence indicates that even eukaryote life stayed pretty simple for a very long time. Plants formed simple algae sheets and mats; animals stayed small and soft; neither left much in the way of fossils. The Earth's oceans were apparently a stable ecosystem for a very long time. Life might have stabilized in those simple forms...
Then it all froze.
The Snowball Period was the worst ice age ever - even the tropical oceans were covered thickly with ice. No one knows for sure why it started, but it had to have left few decent places to live, reduced the producer population drastically, and set off a wave of competition not seen for eons. It lasted for millions of years.
Volcanic gases, accumulating with few plants to remove them, have a greenhouse effect, and that's what probably caused the eventual thaw. From whatever isolated refuges they had used, the surviving animals - now changed - spread out. In the fossil record (the few surviving examples), many new types of animals seem to appear almost instantly; this is called the Cambrian Explosion. All of the major modern animal phyla (and some that wouldn't survive to today) are found in these fossils.
Life was still confined to the oceans, though, so plant life did not have an explosion (and it's hard to tell, since they fossilize poorly). For hundreds of millions of years, life in the ocean developed, some groups moving into the watery ecosystems of the continents like tidal pools and fresh water systems. There, abilities arose that could also be used out of the water: resistance to drying / osmosis; resistance to direct sunlight and rapid temperature changes; exposure to the oxygen levels that had accumulated in the atmosphere (water can hold much less oxygen); moving from pool to pool or against strong currents with sturdier structure.
From these two systems came the movement of Life onto the land of the continents. This is when plants made their major evolutionary leap forward, but many animal groups went with them.
Mass extinctions, occasional catastrophic events that killed most species on the planet, often cleared the systems, and what moved back in often came from different groups, such as when the mammals and birds replaced the massive reptiles after the Cretaceous Extinction. In each extinction, something happened to wipe out most of the plants: shading dust from asteroid impacts or major volcanic eruptions, or ice ages. And the food pyramid can't stand with its base removed.
Regional extinctions sometimes occurred when separate ecosystems connected (as when Panama formed between the American continents), or major climates changed (that connection dried out much of Africa, providing new niches that our own ancestors exploited, evolving from small forest dwellers to walking, hunting creatures of the grasslands).
One thing unlikely to bring about major extinctions is disease. Diseases may wipe out small vulnerable populations of particular species, but two things restrict their extinction potential: first, diseases virtually never affect wide ranges of different types of organisms (and even with small ranges, the effects vary from deadly to nothing); second, diseases themselves evolve. They need to spread offspring, and the less ill they make their hosts, the more likely that is to happen. In most cases, diseases are most serious when they move into a new host type (they aren't well-adapted to the new system and mess up its chemistry), but over time the disease will get more and more mild. It may produce illness symptoms to help its offspring spread (like a cold or flu making us cough and sneeze), but these are rarely serious.
Endosymbiont Theory from an earlier chapter.
More on the endosymbiont theory and early developments in Life.
Early algae evolution.
Evidence for earliest animals.
Evidence for Snowball Period (but was it really snowy?).
First in a video series on early Earth conditions, including Snowball.
Animals from the Cambrian Explosion (video).
Cambrian Explosion explained (video).
Plants move to land (video).
Major extinction events.
Extinction events and living groups.
Can humans bring about a mass extinction (video)?