Coyne begins with the basics: what is a theory in science? One of the mantras of the creationists is that evolutionary theory is "just a theory." Saying that labels the speaker immediately as someone who lacks a basic understanding of science and how science works. Of course evolutionary theory is just a theory, just as gravitational theory is just a theory; so what? In science a theory is a possible explanation or collection of related explanations used in an attempt to understand a fact or phenomenon. Evolution is a fact; the evidence is all around that organisms evolved and continue to evolve; evolutionary theory explains evolution.
But more than explain a phenomenon, a scientific theory has other properties: it has to be testable, or potentially falsifible. In the case of evolutionary theory, when we're surrounded by ongoing, continuous evidence of it happening (pandemic influenza A(H1N1) 2009 being the most recent example to spring to mind), what would falsify it? Finding fossils known to be from organisms that lived in one distinct geologic era embedded in rock side by side with organisms from another could do it. An obvious example would be fossilized mammals, which first appeared about 250 million years ago, embedded in geologic strata from a much earlier time period, like the Silurian (over 400 million years ago). This is one reason some creationists will go to extraordinary lengths to try to prove that humans co-existed with brontosaurs (they apparently think The Flintstones was reality tv).
Another way to disprove a theory is to use it to make predictions -- and if the predictions don't come true, then the theory may be fatally flawed. Unfortunately for the doubters, evolutionary theory to date has proved remarkably accurate in its predictions. A criticism of evolutionary theory used to be that various transitional forms did not exist, e.g., if, as scientists claimed, creatures like whales evolved from land mammals then there should be fossilized whales with legs. I know a few folks who were quite proud of making that argument 20 or 30 years ago. Bad news for them: paleontologists have found a veritable plethora of legged whales, the transitional forms between land mammals and marine. Evolutionary theory predicted not only that such forms would be found, but in what geologic era.
In short, Coyne's book explains evolutionary theory and provides numerous examples to support it. The book is extremely readable and loaded with interesting tidbits from the history of science and the natural sciences. Unfortunately, as Coyne himself admits, even though one would think so much compelling evidence would help to change a few minds, it probably won't.