How and where you cite depends entirely on your audience. For school reports and academic/scientific papers, you use formal citations both in the body of the text and in footnotes or endnotes.
You're writing a popular science book. Formal citations will slow down the reader and probably turn most of them off. You want prose that catches the imagination and engages your reader, not prose that the reader has to slog through.
The length of your work matters too. It's easier to read a work with full citations if it's short. A paper vs a book.
Use endnotes. These are part of the appendix and go after the book is complete. Divide them up by chapter and list them in the order that they appeared in that chapter. You can add page numbers to each endnote entry if you wish, or you can number entries in the body of the text (like a footnote). Adding numbers in the text is distracting so only do it if the chapters are long and there's no other way to make the information clear.
You might want to use both footnotes and endnotes. The footnotes for short but important references or asides and the endnotes for longer ones only of interest to a few.
Use some references in the body of the book. For example, you will mention names of people involved in the work you're discussing and you might give the name of an important book. If the person or book is part of the history, vs just the place where you got the information, include it in the text. Otherwise, save it for the end.
A bibliography is another method for citations. This works well if you mention authors and titles in the text, but is also helpful even if you don't. You can include a line describing the contents and/or importance of the work if you wish.
A good example of a scholarly nonfiction book written for a popular audience is A History Of The World In Six Glasses. The chapters only occasionally mention references and they leave out a fair bit of detail, that only some people would want to know. But the endnotes include all that, plus there's a bibliography. This allows readers to just sit back and enjoy the book, but to delve more deeply if and when they choose.
Find books that have a similar market and scope to yours, even if the subject is completely different. See how they handle the issue of citations. Some authors to check out: Sam Kean, Frans de Waal, Jean Manco, Michael Pollan, Barbara Natterson-Horowitz.