Jemma, this is a fantastic question.

People for hundreds of years have recognized that living things do change form and abilities over time – that living things evolve. While evidence like dinosaur bones and the domestication of animals by humans suggested that living things must evolve in some way, people in the 19th century did not agree on how evolution happens.

The inadequacy of previous explanations and numerous insightful observations about the world led Charles Darwin to develop a superior explanation, evolution by natural selection.

Darwin’s idea combines a few claims about the world:
(1) all organisms are in competition over limited resources, especially opportunities to reproduce;
(2) organisms exhibit individual differences, few are totally alike;
(3) differences can be passed down in genes, for instance children resemble their parents;
(4) some individuals had traits that enhanced their ability to reproduce, better eyesight for example;
(5) those traits that enhanced an organism’s ability to reproduce then get passed down to offspring more often, and eventually that trait will become standard among the species –evolution has then occurred.

Evolution by natural selection best explains the diversity and complexity of life on Earth. The environment acts as a filter, determining which genes are successfully transmitted to the next generation: animals evolved and continue to evolve by descent with modification.

Good question. There are four different ways that evolution can happen. These are:
(1) mutation, by which alleles (copies of genes) get transformed into new alleles by ultraviolet, chemical alteration, etc.
(2) genetic drift, which is random differences in survival between individuals that happen to have different alleles,
(3)
natural selection, which is individuals with some alleles surviving more because of their alleles and is not random, and
(4) gene flow, which is populations containing different alleles intermingling and so causing their alleles to move between populations.

All four of these processes exist in nature. For example, in humans, the ancestors of our species all had brown eyes. Ten thousand years ago or so, a mutation occurred in the Black Sea region that created a human strain that had blue eyes. In Europe and northern Asia, this blue-eyed strain survived more because there is less ultraviolet light far from the equator, so it became common among Europeans and Russians by natural selection, but it did not survive well closer to the equator, which is why Iranians and other southern peoples still have brown eyes.

Peoples around the Mediterranean traded and intermarried, which is how brown-eyed people are present in places like England, and European colonists traveled to America and took their blue eyes with them, an example of gene flow. Finally, Europeans and Americans have largely stable birth rates thanks to societal changes which is not true in Africa and southern Asia where almost everybody is brown eyed, but these changes are not a consequence of eye color, making this rapid expansion of brown-eyed peoples an example of genetic drift.

Because natural selection is the only way that evolution can happen that is not random, all complex adaptations had to have come about or proliferated as a result of natural selection, but the true story is almost certainly more complicated than just natural selection in the vast majority of cases. In many cases, the details are still very murky. Blue eye color in humans is recently evolved and simple, so the story is (relatively) obvious. We do not know yet, for example, how intelligence evolved in humans, and the same is true of a great many other traits in other animals (and plants and fungi and bacteria and viruses and everything else that can evolve).