This is an extremely interesting and extremely fundamental question, indeed, and thus far, biologists have failed at coming up with a satisfying answer.
We know that all the parts are there, we just don't know how they were arranged, or which ones go where.
The question is, in essence, composed of three sub-questions:
- How did the fundamental building blocks of life come about?
- How did the first self-replicating molecules come about?
- How did cell membranes come about?
The answer generally takes the form of "On primordial Earth, a small selection of the billions of organic compounds generated when UV-light hits a mess of carbon dioxide, nitrogen and water where captured in a tide pool where concentration and foam led to random chance producing self-replicating molecules in proto-cells."
This answer, while almost certainly true, is also incredibly dissatisfying, because all it tells us is what deductive logic has already taught us, almost intuitively.
Incidentally, the fact that all of this happens with a million to one odds isn't a problem: The Earth is big, and the time frame for this happening is along the lines of hundreds of millions of years: Anything that might happen once per year by a million to one shot would likely happen hundreds of times in that timeframe.
In any case, when it comes to evolution, or Darwin's Theory of Evolution, or any other theory of evolution, this is all irrelevant.
Evolution is something that happens in any sufficiently complex (open) system, assuming it has the capacity to change at all.
It is most easily observed in living organisms, because they are at the right scale, and incredibly diverse, but it happens on all scales of the universe.
In fact, the easiest way to explain how life first originated, is just to keep counting backwards when you reach the Last Common Ancestor (of All Life on Earth), and propose models for how this proto-bacterium could be even simpler, until you're left with CO₂, N₂ and H₂O, and other simple molecules.
At that end of the spectrum it is well-understood that e.g. H₂O "evolves" from H₂ and O₂, because H₂O has a quality that makes it more "fit" than either of its components, chemical stability.
Furthermore, H2 "evolves" from free hydrogen by a similar mechanism, and free hydrogen "evolves" from protons and electrons, because it has the property of being electrically neutral, which is also a desirable property.
Of course, at the level of protons and electrons, things get a little muddy, and evolution kind of breaks down as a method for explaining how things come about.
Edit: For reference: Current Models of Abiogenesis on Wikipedia.