The answer to this question is found in the Prologue. It beings on p. 18 of the paperback edition of the book. Diamond discusses three common answers that he does not agree with and one that he thinks is accurate, but which does not really answer the question.
The first answer is based on race. This answer says that the Europeans were simply racially superior to the New Guineans and other such people. It holds that Europeans are naturally more intelligent than the “backwards” people and that this superiority allowed them to dominate.
A second answer, found on p. 22, is geographical. It says that Europeans came to dominate because their homeland has a colder climate. It is easier to live in a warm climate than a cold one, so tropical people did not have to work hard to innovate simply in order to live. As Diamond gives the argument:
… cold climates require one to be more technologically inventive to survive, because one must build a warm home and make warm clothing, whereas one can survive in the tropics with simpler housing and no clothing.
The third answer also begins on p. 22. It says that civilization could only arise in river valleys in dry climates. In those places, large-scale agriculture was only possible if there was a centralized government. This forced people to become civilized.
The final answer is one that Diamond agrees with. It says (on p. 23) that “European guns, infectious diseases, steel tools, and manufactured products” were what allowed the Europeans to dominate. Diamond agrees, but says that this is not a real answer because it does not tell us why the Europeans came to have those things when others did not.