This process is explained in detail in a blog post by Nathan W. Murphy.
Google has scanned millions of books that are both (1) out of copyright and (2) still under copyright. If you happen to find a book that is out of copyright, i.e. published before 1923, you’ll usually be able to read the entire book for free online and you do not need to use FamilySearch’s free lookup service. For books still under copyright, i.e. published since 1923, Google Books often provides a “snippet view” or limited view of the pages with your search term or terms. Since you cannot see the entire book online, only a snippet of the page, what if you want to see the entire page, or several pages from the book? The answer — use FamilySearch’s free lookup service.
This will only work if the book happens to be in the Family History Library Catalog, so you need to search for the book first to see if they have the book. If the book is available in Family History Library collection, then you must complete their online Photoduplication Request form and the copy of the page you indicate will be sent to you by email.