Natural selection which is also called survival of the fittest is when a species has an adaptation that makes it better able to survive, reproduce, and pass on it's genes. When it says survival of the fittest, it doesn't mean that only the strong survive. It means that those species with the best adaptations are the ones that are best able to pass on their genes. Natural selection happens in the environment because those with the best adaptations to survive in the environment are the ones who are able to pass on their genes so more animals like them are born.
The first theory of evolution is biogeography. Biogeography is the geographical distribution of species. Biogeography shows examples of evolution because there is scientific evidence that there used to be one big continent called PANGEA. Then all the plates began to move so there are seven continents. But what scientists have found is that where PANGEA used to fit together, the fossils are similar. This proves it because even though the species aren't alike now, at one point they were and then as the continents drifted, the species were forced to adapt and change to survive in their habitat. Also another example of biogeography is islands that are close to each other that have native species that are close to each other. The native species are the same, but the descendents of those aren't because they were forced to adapt to their new environment.
The second theory of evolution is fossil records. Fossil records are molds and impressions of ancient species. Fossils are really great examples of evolution because fossils are imprints of bones found in deep layers of rock. They show evolution because they show bacteria first. Fossils appear in oldest to youngest in order. It shows the changes throughout time. It shows what it started as and what it evolved to. Also because of fossils it's possible to see the transitional forms like changes in skull size and shape.