There is no set time table for the appearance of a new species. According to the well supported theory of punctuated equilibrium (PE), most of the evolutionary changes we see in living organisms occur during the time when an existing species (or in most cases a small population of an existing species) gives rise to a new species. According to Eldredge and Gould, the authors of the 1972 paper proposing PE, the process happens relatively quickly, well within the ~5,000 year resolution limit of the fossil record. Once a new species evolves, it changes little, if at all, until it becomes extinct, to be replaced (or not) by a descendant species that is clearly different but also clearly closely related to it. In fact, the evolution of humans supports PE, as our ancestor, Homo erectus, first appeared in the fossil record about 1.8 million years ago. It changed very little over the entire lifetime, until it became extinct about 70,000 years ago, about the same time that Africans migrated out of Africa to occupy the rest of the world. Homo sapiens evolved about 150,000 years ago in Africa and the earliest skeletons are identifiable as modern humans. Of course there are some minor changes since modern humans first evolved, such as the flatter and broader faces of East Asians, and the shorter limbs and rounder torsos of cold-adapted populations like Eskimos and Northern Europeans, but these differences are not enough for a new species to be recognized.
As Eldredge and Gould point out, the old idea that evolution occurs gradually over a long stretch of time is not supported by the fossil record, and most scientists agree. Nevertheless, exactly how quickly a new species can arise is still under debate. Some suggest that it may take only a few hundred or a few thousand years, but others disagree. We do know that some new species have evolved since the end of the last ice age, which happened about 13,000 years ago. For example, 13,000 years ago, Death Valley in California was a large glacial lake. Yet today it is one of the hottest places on earth, with a small fish, known as the desert pup fish, having evolved to adapt to the hot temperatures. That means the desert pupfish evolved only within the last few thousand years at the most.
As to exactly when a new species should be recognized, scientists often disagree. People who read the scientific literature often come across disputes as to whether an island population should be classified as a different species because of minor differences from mainland populations. Many scientists also categorically reject the subspecies concept and they try to eliminate it by either lumping existing subspecies together or they split them into different species. Such intolerance is more ideological than scientific. Therefore many scientists disagree and continue to recognize the subspecies. Putting aside difficulties with the Biological Species Concept (BSC) when dealing with asexually reproducing organisms, most scientists do accept the BSC, which states that a species is one or more populations that actually or potentially interbreed, and they are reproductively isolated from other populations. The reason for that concept is that it fits what we observe in nature. Even though there is no one around to jail or executive individuals that mate with individuals from other species, most individuals in the wild simply refuse to do so. If you go to a duck pond, for example, you see ducks of the same species pair up, but you won't see individual ducks belonging to different species pair up. The same is true in a forest filled with different species of birds. They won't cross species lines. The reason for animals to be so reluctant to mate across species lines is that each species is superbly adapted to a particular way of life. For example, there are ducks that dabble and feed in the shallows, and there are diving ducks that feed below the surface. If two species adapted to different ways of life were to mate, then their descendants would be somewhat intermediate. A duckling with a diving duck mother and dabbling duck father may not be able to dive or dabble well enough to stay alive. If so, then natural selection would eliminate these hybrid ducklings. That means individuals that do not observe species boundaries will end up leaving fewer or no descendants at all. That is why many species have evolved ways to make sure that individuals recognize each other as the same species before they agree to mate. The different songs and plumages of birds are ways to identify individuals of the same species.
If each species is adapted to a particular way of life, then why do new species evolve? The reason is that individuals of the same species all have the same needs. As the population nears the limit the environment can support, competition for survival becomes fierce. One way to stay alive is to start exploitin resources that are new. For example, when the ancestor of Darwin's finches first inhabited the Galapagos Islands, they all ate the same thing. But as the population grows, some birds were probably forced to start eating different things to have enough to eat to survive. To eat different foods, a bird may need a new kind of bill. For example, a seed eater may need a short and thick bill to crack nuts, and a nectar feeder may need a long thin bill to drink the nectar. Even though the original birds that started eating a different food may have the wrong bill shape. Because of the absence of competition on that island, these individuals can get by for the time being until mutations happen through chance to make their bill better suited to processing the same food. Such a mutation would have been eliminated if the birds was still eating the old food, but it is most welcome when the bird has started eating the new food. This and other mutations that change the bill to suit the new food will then be welcomed, and they will spread. IN this way some individuals of an old species can be well on its way to becoming a new species. All that it needs is some way to avoid interbreeding with the old parental species to preserve these new adaptations. So, if a mutation changes the song or plumage of these individuals, they can be considered a new species, since they no longer interbreed with the old one. IOW, they have become a new species under the BSC.