Transparent, Logical, Flowing, Informal, Unassuming
Something remarkable about Tolstoy's writing style is how unassuming and hard to notice it actually is. There are very few words that would send you scampering to a dictionary, almost no flowery or lush descriptions, and not much in the way of long, winding or intricate sentences. Simple words and short, easy sentences are much preferred. In fact, Tolstoy would often avoid using an extensive vocabulary and choose to deliberately repeat the same everyday word many times over in a single passage rather than use a different one. (His older translators often didn't respect his decisions.)
On the larger scale, Tolstoy's prose is remarkably logical as well. You can often divide it into units (not always paragraphs) which begin with a very short, stand-alone summary sentence, then gradually expand to a cluster of closely connected sentences where all the details get thrown in. Finally the whole thing contracts to another short, stand-alone summary sentence. The four-paragraph passage beginning "Ivan saw that he was dying…" at the start of Chapter 6 is a perfect example of this.
Ivan Ilych saw that he was dying, and he was in continual despair.
In the depth of his heart he knew he was dying, but not only was he not accustomed to the thought, he simply did not and could not grasp it.
The syllogism he had learnt from Kiesewetter's Logic: "Caius is a man, men are mortal, therefore Caius is mortal," had always seemed to him correct as applied to Caius, but certainly not as applied to himself. That Caius – man in the abstract – was mortal, was perfectly correct, but he was not Caius, not an abstract man, but a creature quite, quite separate from all others. He had been little Vanya, with a mamma and a papa, with Mitya and Volodya, with the toys, a coachman and a nurse, afterwards with Katenka and will all the joys, griefs, and delights of childhood, boyhood, and youth. What did Caius know of the smell of that striped leather ball Vanya had been so fond of? Had Caius kissed his mother's hand like that, and did the silk of her dress rustle so for Caius? Had he rioted like that at school when the pastry was bad? Had Caius been in love like that? Could Caius preside at a session as he did? "Caius really was mortal, and it was right for him to die; but for me, little Vanya, Ivan Ilych, with all my thoughts and emotions, it's altogether a different matter. It cannot be that I ought to die. That would be too terrible."
Such was his feeling. (6.1-4)
Tolstoy's writing also has a strong sense of flow thanks to several techniques he uses to tie his sentences together. He might repeat a similar structure from one sentence to another (the string of questions in paragraph three, above); he might express one idea or thought across several short sentences (as in the last two sentences of paragraph three, above); or he might start his sentences with conjunctions or other words that link to the sentence that came before ("that," "and," "but"). For an example of that last technique, check out this beginning of a paragraph:
The pain did not grow less, but Ivan Ilych made efforts to force himself to think that he was better. And he could do this so long as nothing agitated him. But as soon as he had any unpleasantness with his wife, any lack of success in his official work, or held bad cards at bridge, he was at once acutely sensible of his disease. (4.16)
If you look closely, you'll see that many of Tolstoy's sentences start with "and," but," or "that." This further shows that Tolstoy really didn't have a problem with informal writing.