How do species adapt to their environment?

For example, imagine a normal white person consistently exposed to the sun. The higher and constant stimulus provided by the new environment (i.e. larger amount of radiation) forces the organism to produce more melanin, the related skin and tissue protein which protect the respective tissues and body from excessive incoming and dangerous sunlight. So, there's a tendency to produce more and more melanin, but its production is limited to the genetic capacity to response on this phenomena. A person who have albinism $\text{could not}$ response in these ways, because there's $\text{NO}$ genetic basis to produce melanin!
Also, you could hypothesize living beings fitting low air moisture and pressure, different average temperatures, soil constitution, concentration of solved oxigen in water or atmosphere, and so on. The response generated varies, comparatively, on the driving forces of the biotic and abiotic environmental pressure (weak, moderate or strong) and the own capacity to produce immediate responses to the new facing stimulus. That kind of immediate and specific response is called $\text{acclimatization}$, and it's related to the phenotypic plasticity of the organism.
$\text{Adaptation}$ is, by itself definition, related to the $\text{evolution}$ of new genetic traits on the genome of some population or species, giving them new abilities to response positively to diverse environmental stimulus. Thus, some species will only adapt to new conditions if their modified genome evolve in this new environment, fixing the new aleles/genes related to that kind of phenotype response.