The Best Ways to Research for a Book
You want to make sure the information you seek is correct, valid, and backed up by evidence. The best way to do that is by searching in reputable sources.
Start big and then narrow your focus.
Start with the history of the subject. Find big, broad range sources such as encyclopedias or dictionaries. These are generally reputable sources that give you a good base of information on which to build for any particular subject.
Try the Library for broad range sources of information. Limited in what they carry by their physical space, they have to be pickier about what books they choose to hold. Finding one great book in a library can spur a large list of similar books related to your topic by scanning annotations and footnotes.
Though a fantastic source, be careful using Wikipedia as all information may not be correct. You might want to find equally reputable sources to corroborate the information on Wikipedia.
Be careful using the internet as a source as well. One can find thousands of articles and fantastic sources, but must also be careful to check for reputable sites and authors, which isn't always easy to discern. As with Wikipedia, check several sites for the same information. Dig into the authors to make sure they know what they're talking about instead of just trolling.
Once you have wide base of general information about your topic, you'll want to focus down a little.
This means diving into journals, newspapers, periodicals, specialized areas of study, and experts in those specialized areas. Always be polite and helpful when contacting experts or eyewitnesses. Be flexible in setting up an interview or mode of communication as most people are busy.
Be sure to gather many perspectives.
And remember that if you're writing nonfiction, cite your sources so readers can follow up on the information presented but more importantly, so you're not plagiarizing.