A warning -- Hume wrote so beautifully, with such concision, clarity, precision, and elegance, that the temptation is overwhelming simply to incorporate large chunks of the Treatise into this tutorial. Any student of philosophy who imagines that it is necessary, or even desirable, to write turgidly and obscurely when engaging with deep questions would do well to spend a long time reading Hume and striving to emulate him.
Students striving to emulate Hume's writing style is exactly what one doesn't want. Hume has many virtues, and it is certainly often said that he writes with clarity and precision, but all the actual evidence is that he is not, in fact, very precise, and that his clarity is largely superficial. As I've noted before, Hume was effectively writing in a very different dialect than he spoke; Scots English in the eighteenth century was much farther from the English of England than the two are now. Hume, being an intense Anglophile, put considerable effort into it, and thus became one of the best Scottish writers of English English. But he was still some distance from the summit, as can be seen if one compares him to his critic James Beattie, who really does write beautifully, clearly, concisely, precisely, and elegantly (even if not always so insightfully) and is hands down the best Scottish writer of English English in Hume's day.
Don't get me wrong: Hume has many virtues as a writer -- his figures of speech are often very striking, his sense of vocabulary (into which he put an immense effort, due to the dialect differences just mentioned) is excellent, and his powers of large-scale organization of his text are much better than usually recognized. But his prose is notoriously ambiguous (sentence after sentence can be read in different ways, to such an extent that the history of Hume scholarship sees Hume being interpreted in radically, and I mean radically, different ways), his discussions sprawling enough to make his (often quite good) organization difficult to see, and when some of his contemporaries ridiculed him for putting things oddly (his occasionally French-sounding syntax, his rampant egoisms, etc.), they did have something of a point.
Hume's virtues as a philosopher include perceptiveness, not elegance; acuteness of observation, not precision of reasoning; striking presentation, not beauty of language; organization of inquiry, not conciseness of argument; restraint in description, not clarity. To be sure, there are passages in Hume that are beautiful, or concise, or elegant, or precise, or clear; he improves greatly in his later works; and he has been helped out by the increasing distaste for rhetorical flowers and balanced clauses, as well as by the slow homogenization of English. But if beauty, concision, elegance, precision, or clarity are what are important to you, Butler and Berkeley are better role models on every single point. Hume's strengths, though lying elsewhere, are really and truly strengths; they have their place, and are not to be dismissed lightly. But the claim that Hume is somehow a particularly elegant and clear writer is mostly a myth of the twentieth century.