Charles Darwin believed that all animals have descended from at most four or five common ancestors (Darwin p. 503). Science technology has not advanced to the stage it had back then but he was convinced of his ideas through his observations of animals. He observed two similar crab species working together to attain food, similar behaviors between bird species in separate continents, variation among current living species, and the fossils of extinct species who carried many similarities with current species (Darwin p. 496). All this evidence ascertained his belief in natural selection and that each generation of species comes with a great number of variation and the ones with traits best suited to their survival pass on their genes to future generations. His belief are founded in three main arguments: in each generation plant and animal species are subject to variation, there has been no clear distinction between species and well-marked varieties, and that certain species are capable of being interbred (Darwin p. 498).
The most convincing argument to me was the amount of variation which could be observed even among current species. If it can be believed that variation among generations exists currently then there is good reason to believe it existed in the past. If variation among species existed in the past then it becomes easy to also hypothesize that that the species with traits best suited to surviving were able to survive and pass on their traits to future generations.