Henry Hazlitt's Thinking as a Science, from 1916, is short and has good, practical advice about how to think. I particularly recommend chapters 1 (advocating thinking), 5 (about prejudice) and 7 (about reading). The book is free. Go read chapter 1 (11 pages) right now and see what you think. And Anonymous posted some great book quotes.
My comments on a few passages (these are not representative of the book; emphasis added):
The secret of practice is to learn thoroughly one thing at a time.
As already stated, we act according to habit. The only way to break an old habit or to form a new one is to give our whole attention to the process. The new action will soon require less and less attention, until finally we shall do it automatically, without thought—in short, we shall have formed another habit. This accomplished we can turn to still others.
This is something I've been advocating heavily for years. People learn to do something correctly, once, and then think they've learned it and they're done. But that's just the first step. For skills you'll use often, you have to practice until you can do it cheaply, easily and reliably. E.g. I need to be able to type using almost zero conscious attention so that I can focus my attention on the ideas I'm writing. I need to think in an objective – not biased – way pretty much automatically so that I can get on to considering the topic; people who need to use a bunch of mental focus just to avoid bias are handicapped because they have less attention left for the actual topic (and what often happens is, at some point, they focus their attention on the topic and then their habitual bias starts happening).
When I look back into the past, I find nations, sects, philosophers, cherishing beliefs in science, morals, politics, and religion, which we decisively reject. Yet they held them with a faith quite as strong as ours; nay—stronger, if their intolerance of dissent is any criterion.
Intolerance of dissent is not a criterion of strong belief in being correct. It's an indicator of the opposite: lack of confidence in the truth of one's claims. Why suppress dissent when you can win the argument?
If you think a heretic won't convince anyone, you laugh at him and don't care much. If you know the heresy is a threat to your claims, then you try to suppress it.
As William Godwin pointed out, this applies to parenting too. Parents persuade their children with reasoning when they can. Parents resort to using force against their children only when their own rational words fail them.
The practice of Gibbon remains to be considered: “After glancing my eye over the design and order of a new book, I suspended the perusal until I had finished the task of self-examination; till I had revolved in a solitary walk all that I knew or believed, or had thought on the subject of the whole work, or of some particular chapter. I was then qualified to discern how much the author added to my original stock, and I was sometimes satisfied by the agreement, sometimes armed by the opposition of our ideas.”
The trouble with this method is that it is not critical enough; that is, critical in the proper sense. It almost amounts to making sure what your prejudices are, and then taking care to use them as spectacles through which to read. We always do judge a book more or less by our previous prejudices and opinions. We cannot help it. But our justification lies in the manner we have obtained these opinions; whether we have infected them from our environment, or have held them because we wanted them to be true, or have arrived at them from substantial evidence and sound reasoning. If Gibbon had taken a critical attitude toward his former knowledge and opinions to make sure they were correct, and had then applied them to his reading, his course would have been more justifiable and profitable.
In certain subjects, however, Gibbon’s is the only method which can with profit be used. In the study of geography, grammar, a foreign language, or the facts of history, it is well, before reading, simply to review what we already know. Here we cannot be critical because there is really nothing to reason about. Whether George Washington ought to have crossed the Delaware, whether “shall” and “will” ought to be used as they are in English, whether the verb “avoir” ought to be parsed as it is, or whether Hoboken ought to be in New Jersey, are questions which might reasonably be asked, but which would be needless, because for the purposes we would most likely have in mind in reading such facts it would be sufficient to know that these things are so. We might include mathematics among the subjects to be treated in this fashion. Though it is a rational science, there is such unanimity regarding its propositions that the critical attitude is almost a waste of mental energy. In mathematics, to understand is to agree.
The first quoted paragraph is for context. I like the second. But the third is mistaken about math. Mathematicians make plenty of mistakes and have debates and disagreements about what's mistaken. See The Fabric of Reality chapter 10 for arguments on the fallibility of math.
Infinity is an example a contentious mathematical topic. Objectivist philosopher Harry Binswanger denies the existence even of very large integers.
Grammar and history are more controversial topics than math. In my own reading, I've often found rival schools of thought about the interpretation of historical thinkers like Burke or Godwin. The issue arises even for recent history, e.g. there are debates about what Rand's or Popper's personality was like. These debates extend to what certain facts are. Historians debate facts like who wrote a particular book, article or play. They also debate e.g. what information political leaders had at times they made certain decisions, or whether they committed certain crimes or not.
I wrote a recent article on grammar. While researching it, I discovered controversies like whether constituency or dependency is a better way to model grammatical relationships, debates about different ways to interpret words, and even a disagreement about whether verbs are primary in sentences or, alternatively, subject and verb are equally important. And there are a bunch of different lists of standard sentence patterns, most of which are bad because they have a subject+verb+adverb pattern (unlimited adverbs can be added to every pattern, including that one, so it doesn't make sense to have an extra pattern just to include an adverb).