Well truthfully scientists don't know how exactly everything came to exist, there are some theories that say if one adds up all the matter and energy in the universe you get zero so the universe could have come from nothing, although that is just a theory and not proven yet.
now onto fact. Life coming from non-life. In the 1950 a experiment was preformed (which has been reproduced many times) called the Miller/Urey Experiment. In this experiment they basically took non organic molecules CH4 (methane), NH3 (ammonia) H2 (hydrogen) and H2O (water) and put them under similar conditions that the earth was under around 4 billion years ago. They also created electrical sparks in the container to simulate lightning. After a few weeks this setup produced organic compounds, including some amino acids. Now this is over the matter of a one week, if this experiment was allowed to go on for longer it is possible that even more organic compounds could have come from it.
So now we have organic compounds, well we obviously arn't at cellular life yet, so what now. Well basically what is needed next is a molecule that can self replicate using the materials in its environment. It is theorized that the first molecule to do this (note just because this part is theory tht doesn't mean that all of evolution is a theory) was RNA or something very similar to it. The first RNA molecule being made by the random chemical interactions.
OK, so now we have a self replicating molecule, (I won't go into how we believe the first cells were made, because its not important in this context) so we want to know how it can become more complicated and evolve. This is where random mutation comes into play. Lets say that due to a chemical reaction something happens to our rna that makes it less likely to survive, while another rna molecule has a chemical reaction that helps it. (note there will also be many changes that don't do much of anything). Well obviously the one with the benefit will survive over the one with the disadvantage. So we start a trend where beneficial mutations help the molecule survive and as these mutations occur it gets more and more complicated and so on. Remember this is happening over a period of billions of years, so sure the chances of all this happening are small, but its over a very long time.
So that is the basic theory of how life came to exist. Now yes I did call this theory, because there is no way that one can know for sure how the very first molecule and cell were formed. Although the ideas of evolution (ie change through random mutation, and survival of the fittest) are proven facts and there is a huge amount of fossil and genetic evidence that can show evolution over a course of millions of years. This means that we know that life on earth has been evolving, and the theory for the start of life that I talked about in the beginning is a theory that has evidence and follows along with evolution which we know to be true.