A very brief history of time

To answer this question in great detail would be long but I'll try to keep it brief. As far as the matter and energy that comprises the visible universe it has, as far as anyone knows, always existed. It is infinitely older than this universe. What that means about the universe before the big bang we do not know, the big bang itself destroyed all information about the universe before it. At least as far as we know, perhaps when we have a quantum theory of gravity we will be able to find out more, but currently we don't yet have such a theory, we have some good candidates for such a theory but they are still far too incomplete.
The big bang, contrary to popular belief, was not an explosion, it was a sudden and rapid expansion of space-time. As the universe became less dense it also became less hot, allowing the four fundamental forces of electromagnetism, gravity, and the strong and weak nuclear forces to separate (possibly) and for the formation of the two lightest atomic nuclei, Hydrogen and Helium. These formed around 100,000 years after the big bang. Gravity is actually the weakest force in the universe which we can easily confirm by dropping something from just about any height. The electromagnetic force is what keeps things from passing through each other and no matter how high something seems to fall from it never falls with enough force to break the electromagnetic force, but the electromagnetic force is more than strong enough to counteract gravity, just put two torus shaped magnets around a pole with the same poles toward each other and you will see one magnet levitate.
when the universe cooled off further hydrogen and helium nuclei started attracting electrons and making atoms. After further cooling gravity could begin to assert itself and the hydrogen and helium clouds started to collapse into stars, the galaxies we see are most likely the result of the universe in what appears to our current mathematical models to be a singularity, the point before the big bang when the entire universe was extremely dense, was "clumpy" it wasn't a smooth or perfect sphere, when it expanded the clumps just expanded too and now make up the galaxies.
So after the hydrogen and helium started collapsing into stars in those areas where things were clumpiest in the young universe, we know that stars work by nuclear fusion, they are so massive and dense that hydrogen in their cores is converted into helium, releasing energy in the form of photons, which is why our sun glows so bright. But when you fuse two hydrogen atoms you get a helium atom. Deep within a stars core there is also enough pressure and energy to fuse heavier atoms, in fact every element can be fused deep within the core of the most massive stars. The larger the star the shorter the lifespan, this is because more massive stars tend to burn hotter and so they tend to burn themselves out faster. These stars are also more likely to supernova. These supernovae would eject large amounts of heavier elements into the universe to be used in the formation of the next generations of stars. Our sun is a third or fourth generation star, it is only about 4.5 billion years old. The universe is about 13.7 billion years old. Our solar system's accretion disk also had a lot of heavier elements in it which while the disk was spinning was flung out to the outter edges of the disk as tends to happen, the majority of the matter was still concentrated in the center and formed into the sun, the planets solidified from the material that was imperfectly distributed along the outskirts.
There was, of course a lot of debris in the early solar system shortly after the earth formed, and an almost Mars sized celestial body impacted the earth around 4 billion years ago while the earth was still molten enough to reform after the collision which resulted in a chunk of the earth flying off and forming the moon. Meanwhile Jupiter and Saturn are working hard to attract as much inner slar system debris as possible but there is still a lot in the inner solar system which hits the earth as meteorites. Actually occasionally even to this day Jupiter and Saturn will accidentally fling something into the inner solar system, but for the most part their massive gravitational fields tend to attract meteors from the inner solar system to them.
Water is the most abundant chemical in the universe as hydrogen is the most abundant element in the universe and water is the simplest compound. Because of the nature of how objects collapse into planets and stars the earth acquires it's rotation. The denser elements will tend toward the center so we have a dense nickel iron core which is seperated into an inner and outter core, the inner core is hot and liquid due to the amount of pressure above it, seems paradoxical but that's how it is. The inner core rotates at a different rate than the outter core working like a dynamo and generating a massive megnetic field. It also, along with the molten mantle, helps to drive plate techtonics. Another source of energy that helps to drive plate techtonics is radiation from the decay of radioactive materials.
Meteorites and comets impacting the young earth's surface brought with them water and many of the biochemicals necessary for life. This was proven when scientists analyzed the crater of a meteorite to see what the meteor was made of and found many of the amino acids and nucleotides found in all life on earth. Then there is the even more recent analysis of the deep impact probe that crashed into a meteor in space and a spectrum analysis of the debris that flew off confirmed that the meteor did indeed have amino acids and nucleotides on it.
The early earth's atmosphere was supplied by the young planets geological processes, volcanoes and other processes that spewed lots of toxic gases into the atmosphere...toxic to us, that is. The early atmosphere had very little O2 and O3 in it and as a result the amonia and methane and hydrogen that did make up the majority of the early atmosphere couldn't bind to a lot of oxygen and become stable. The introduction of energy from the sun and from sources like lightning resulted in more of the biochemical compounds necessary for life forming. At this point our understanding is less certain about what followed. What we do know is that self replicating polypeptide chains form easily when the necessary amino acids are present. DNA and more simply RNA is a great way to streamline the process. Cells can exist without DNA or RNA but they would not have inheritable material in them. The DNA or RNA allows for inheritable material being introduced into cells which would be mutually beneficial to the DNA which is kept together and safe in the cell and to the cell which can now reproduce itself. How specifically all of this happened is the subject of an ongoing research subject called abiogenesis, though, and I don't know all of the current theories.
Once the first organism did come about with inheritable material, though, then it was a simple matter of natural selection. The first organisms would have just consumed amino acids and most likely repriduced asexually possibly getting genetic material from other organisms like themselves that they ate. Mutations happen from transcription errors or radiation. In more complex organisms entire sections of DNA may be added or deleted. Whole chromosomes may be duplicated or sometimes two chromosomes may be fused into one. Natural selection simply means that nature will determine which organisms survive and which do not. Those organisms which are unfit to compete in a given environment are less likely to survive to reproduce. Like bacteria in a petre dish, if you introduce penecillin, those bacteria with no genetic resistance will die and are less likely to reproduce, while those which are resistant are more likely to survive to reproduce. Over time random mutations will improve resistance until the bacteria are completely immune.
Over time these small changes accumulate and a new species emerges. Given more time more information will be added to the genome and even more complex structures will emerge. I could go into greater detail but this is long enough.