Logic and Contemporary Rhetoric by Howard W. Kahane and Nancy Cavender, a great textbook to learn about reasoning, logical fallacies, and how to avoid being taken in by bad arguments in things like advertisements and political appeals.
I’ll second this one as a great book, one of my high school teachers had it as required reading for the class. The only qualm I had with it was that his chapter on class-ism was very clearly heavily tainted by his personal views, and the “studies” he cited to prove his points were patently absurd. For example, one study he used measured how long it took for someone to honk at the car in front of them after a stoplight had turned green, and then broke this down by the price of the car. Kind of surreal, after all the skeptical stuff in other chapters.
Well, if you want a really classic one, how about The Discoverie of Witchcraft by Reginald Scot, first printed in 1584? Scot, admittedly, takes a lot of things on Christian faith, but his basic thesis is that witchcraft does not and cannot exist, and to prove it he interviewed magistrates, applied a sharply skeptical eye to certain passages from the Bible, and talked to street magicians to find out how conjuring tricks were done. A fascinating read, 400-odd years later.
Even more classic is Lucian’s circa 2,000 yeatr old piece on “Alexander, the Miracle Monger” – an expose on a fake mystic during Roman times. Lucian goes into some detail about how they worked fake miracles. It reads like something Martin Gardner or Randi would write today. Lucian was a noted author of satires (and they’re well worth reading, too), but his work on Alexander seems to be real reporting – they’ve found some of Alexander’s souvenir “relics”.
My copy of Lucian is the (I think now out-of-priont) Penguin edition, but the Loeb Classical Library version of his work is still in print.
For examples of being sceptical about specific subjects, there’s various writings by Frederick Crews, including Follies of the Wise, in particular his essays about Freud and psychoanalysis.