If a book's author does not cite sources for its information then I think that you will need to start searching the historical records until you find the information that you are trying to verify.
I recommend starting with pieces of information that are close to the present time to double-check that the ancestors you find are actually those that the book asserts them to be.
Starting with the earliest purported ancestors may lead to much effort being wasted learning about people who you later find are not your ancestors.