It wasn't "out of nothing," of course. There had to be at least a supply of energy sufficient to produce the fundamental particles of matter.
Matter has mass, and therefore tends to clump together. Big clumps can be compressed sufficiently by gravity to ignite nuclear fusion in their cores, producing stars. The fusion, and particularly the fusion events associated with cataclysmic explosions of stars (that is, novas), over stellar generations produces a wide range of different chemical elements.
Some of these elements form very complex compounds, and arrangements of these compounds can actually become self-replicating in suitable ambient conditions and the presence of sufficient additional materials. That is, they can form primitive life forms.
Because the replication of life forms is not always exact, they can include variants. In some conditions, certain variants may survive and reproduce more efficiently than others, and therefore dominate the population. In other words, a population of life forms may evolve over generations--and the resulting population may evolve again, and so on. Dramatic developments can include cellular structure, multicellular forms, multicellular forms containing specialized structures and organs, and so on.
Conditions which lead to evolutionary change can include, in addition to external circumstances such as climate, predatory forms, and food sources, the interactions among individuals within the population. Social interaction and communication can even determine the favored direction in which to adapt.
These processes account not only for the human body, but also the human mind.
As this is R&S, I will also comment on my point of view: I'm a lifelong Christian. Nothing in the above description denies the possibility of a Creator, but it does suggest that if (as I believe) such a Creator exists, he's a whole lot more clever and inventive than creationists give him credit for.