How do you write a nonfiction book?

That is definitely true. You will likely have to get permission from said authors and publishers if you need to cite a certain percentage of their work.

Since you're vague on the subject of this hypothetical book. It all depends on your subject. Academic libraries (university level) is clearly the best start. More info about the topic is needed.

Yep, it's libraries, source material, etc. This can include interviews, that sort of thing.

If you were writing about, let's say, the basketball program at Duke, you would interview coaches, players, player spouses and significant others, professors, fans, boosters, etc. You would look at historical society records for the area or other information on the school, the city, etc., if you were covering that angle, that kind of thing.

If you were writing an historical work, and you quoted William Preston Johnston on his conversations with R. E. Lee, you don't need permission. Johnston died over a century ago, and even his private correspondence is in the public domain (which is to day, no longer under copyright). If you quoted the Tsar Stepan, there are many circumstances in which you would not need permission. So, for example, Stepan might criticize Anne Curry's thesis on the balance of forces at the battle of "Agincourt" [sic], and you can use that citation without permission. In such cases it it ordinary to inform the publisher--you don't need permission because you are citing someone in a scholarly work. Commonly, one informs the publishers of the work as a courtesy only.

There are two ways that history gets written. One is to present new evidence, and the other is to present a new interpretation. In 1943, in the second volume of Lee's Lieutenants: A Study in Command, Douglas Southall Freeman cited the manuscript memoirs of Kyd Douglas (Henry Kyd Douglas). He did so with permission (either a precaution, or a courtesy to the holders of Douglas' estate--the memoirs had been written long enough before he cited them for them to be in the public domain).

There was much material in Freeman's book that constituted new scholarship--material which had never been published before--such as Douglas's manuscript memoris. At the same time, Freeman was a sufficiently popular writer that his books would have sold well just on his name, even if there were no new scholarship in them. A good example of this is The Civil War: A Narrative by Shelby Foote. He was a fairly well-known author, and popular among the reading public who would have encountered his books that the series sold modestly well, and its popularity grew by word of mouth and good reviews. I don't believe Foote did any original scholarship for the series, but it sold well anyway. All his material was taken from known sources. The Ken Burns television documentary on the civil war, largely taken from Foote's books, just introduced him to a wider audience, and made his work that much more popular.

The other path is controversy. I mentioned Anne Curry above. In 2005, she wrote a book entitled Agincourt: A New History. She was not presenting new scholarship, not in the sense of new material, like Freeman with Kyd Douglas' memoirs. Rather, she reinterpreted the existing material, and came to new conclusions. They were controversial conclusions, too. There are seven contemporary sources for the battle of Azincourt, three of which were, or claimed to be, eyewitness accounts. You're not going to come up with new material (or it is very unlikely that you will), so your only path would be the same as Dr. Curry--to come up with a new interpretation of the existing material.

Dr. Curry is a highly respected historian of the Hundred Years War. That alone would guarantee modest sales--indeed, the battle of Azincourt is a very popular topic in the English historical myth, so that would also guarantee more sales. That same year, Juliet Barker published her own book, Agincourt.. She is also a highly respected historian of the Hundred Years War, and everything i've said about Dr. Curry's work applies to Dr. Barker. Furthermore, Dr. Barker acknowledged Dr. Curry's work, and then declined to agree with her. Holy Controversy, Batman . . . that meant more sales for them both. (Dr. Barker i've seen on youtube--she might be ahead of Dr. Curry right now.)

If you're going to write history, and expect to be taken seriously or to be successful--you'll need either to come up with new material, or a new point of view which will be taken seriously. Good luck.

For an online work, to add to this, I'd also recommend an intelligent link citation, e. g. with a good title.

It would be like:

Anne Curry - The Battle of Agincourt

rather than

book

or

http://books.google.com/books/about/The_Battle_of_Agincourt.html?id=H3V2Qv6E5cEC

See the difference? Not coincidentally, good URL titles are also better for search engine optimization purposes.

Hi Ray C,
It's true that you have to get permission if you want to use someone else work in your book and you have to mention there that you have taken reference from the "Xyz". And you can also prefer online sources to know more about your topic of book writing.