How did life begin?

The short answer is that nobody really knows.

While we have a fiarly detailed and precise account of how life evolved from its initial state as some sort of single-celled prokaryote to the vast diversity of living organisms today, we know very little about how that first prokaryote got started in the first place.

Creationists often try to use this as an argument against evolution, but this makes very little sense; it would be like saying the theory of gravity is wrong because we don't have a solid theory of star formation.

One theory is that life on Earth came from outer space, panspermia, but that really just pushes the question back: Okay, but where did that come from?

Current theories include:

1. Ice sheets during one of the coldest ice ages could have shielded organic compounds from solar radiation, keeping them stable for long periods of time and allowing them to form more complex structures simply by natural chemical reactions.

2. We know that lightning can produce organic compounds in the atmosphere, so maybe lightning in volcanic clouds provided the right conditions for a simple organism to emerge.

3. DNA is very hard to create, but RNA is less so; so perhaps RNA emerged first, populating the world with RNA-based organisms, which then later evolved into DNA-based organisms.

4. Primordial organic chemicals could simply have gradually combined and randomly mixed enough to eventually create a living organism.

5. Hydrothermal vents deep in the ocean contain a lot of energy and organic compounds. They were well-shielded from radiation, and could have provided the catalyst for living organisms to emerge.

None of these are really convincing theories, but a lot of scientists are working on it. It's also important to keep in mind that the universe is very big, and so even a very small probability of creating life on any given planet could nonetheless be enough to ensure that it happened somewhere---and since we're alive, one would expect us to find ourselves on a planet where it had, rather than a planet where it hadn't. (This is an application of the Weak Anthropic Principle.)