How evolution works?

Through mutations and natural selection.
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Evolution favors the most adaptive individual. Adaptive ones have always survived and moved their genes ahead through propagation. If some individual of any organism has had an mutation in its genes (which happens time to time by coincidence), and it has had advantage in life because of it, most likely this individual has survived better than the others and could have produced descendants more easily. So the good mutation has spread through descendants during several generations and has became standard feature of that species. At the same time the others with inferior genes have slowly passed away, because they couldn't had so many offsprings than the strong ones. Like this the natural selection favors the strong ones who are most suitable for their living environment.
And through time new species have developed from the same ancestors, when species have moved to another environments and developed new features suitable for their new needs.
This is the evolution from onecelled creature to human:

In process... my drawings, not evolution (or it is actually always in process)