There are many things that we learn about Sherlock Holmes, one right after the other, in Doyle's "A Scandal in Bohemia," which appeared in Strand and was the first of the Sherlock Holmes stories to be published. The things we learn about Holmes come through the musings and memories of Watson; Holmes's conversations with Watson and others; and Holmes's explanations of his logical observations and deductions. The basis of all that is learned throughout is built in the first few paragraphs of Doyle’s story.
In the first paragraph we learn about Holmes's emotional capacity and his peculiar strain of temperament that makes him the logician and observer that he is:
All emotions ... were abhorrent to his cold, precise but admirably balanced mind. ... the most perfect reasoning and observing machine the world has seen.
We then learn about his "fierce energy" and his unfortunate habit of using cocaine when boredom overwhelmes him--it is interesting in and of itself that Doyle gave this unfavorable trait to Holmes in the strict and rigid Victorian era; one wonders whether Doyle is, as a doctor and writer, pointing out a secret strain of escape from Victorian restraint running through London or simply giving Holmes a very human failing to enhance the character.
In addition, we also learn of some of Holmes's background; e.g., "the case of the Trepoff murder." This is an interesting narrative device employed by Doyle, because, of course, "A Scandal in Bohemia" is the first Sherlock Holmes story and therefore the first Sherlock Holmes case--as he didn't exist previously! We then learn, in relation to Watson's own activities, that Holmes is given to pacing the room when involved in a mystery ("I saw his tall, spare figure pass twice in a dark silhouette") and that he is tall and lean, "spare." We also learn the date of his newest case, "March, 1888," and the location of his abode, "Baker Street," where he and Watson had formerly shared rooms before Watson's marriage, which he associates "with my wooing, and with the dark incidents of the Study in Scarlet" (more of the narrative device establishing a flashback to a background preceding Holmes's creation!).
Finally, in the beginning paragraphs of Doyle's finely crafted story, we learn of Holmes's gift for observing--and trusting his observations--and his gift for deductive reasoning. He observes points of Watson's dress and deduces--correctly!--that Watson has gone back into private medical practice; has gained seven and a half pounds in marriage; has recently gotten very wet and muddy; and has a "most clumsy and careless serving girl." We further learn that Holmes and Watson have a relationship of fondness and mutual respect and good will so that their friendship is indispensable to each other:
Stay where you are [Doctor]. I am lost without my Boswell. And this promises to be interesting. It would be a pity to miss it. ... I may want your help, and so may he.
The remainder of the story adds more details in a similar fashion--woven into the action and the thoughts and the conversations of the participants--to produce a full-blown picture of Holmes and Watson, all built upon the revelations in these first few paragraphs.
Although "A Scandal in Bohemia" was the first short story Doyle wrote about Sherlock Holmes, published in 1891, I would just like to clarify that it was not the first Sherlock Holmes story ever. Two longer stories, A Study in Scarlet and The Sign of the Four, were published in 1887 and 1890 respectively. Sherlock Holmes methods were therefore already established, so the mention of these in "A Scandal in Bohemia" are not so much providing the reader with new information so much as revisiting Holmes' way of solving crimes.
One new aspect of Holmes' personality that is presented in the first paragraph of "A Scandal in Bohemia" is his view on love.
"He never spoke of the softer passions, save with a gibe and a sneer. They were admirable things for the observer -- excellent for drawing the veil from men's motives and actions. But for the trained reasoner to admit such intrusions into his own delicate and finely adjusted temperament was to introduce a distracting factor which might throw a doubt upon all his mental results."
For Sherlock Holmes, love and passion are weaknesses, serving only to cloud judgment and skew focus. For someone so dependent on powers of observation, it is little wonder that Holmes finds such sentiment ridiculous for one in his position, and instead only admires it in others to the extent that it lets him more easily see a man's intentions or motives.
Watson makes it clear that Holmes is a cold man lacking in the usual human passions, echoing a sentiment previously voiced in The Sign of the Four when he tells Holmes "You really are an automaton -- a calculating machine." Watson follows up his observation of Holmes' lack of regard for love with the statement, "Grit in a sensitive instrument, or a crack in one of his own high-power lenses, would not be more disturbing than a strong emotion in a nature such as his." In this way, he gives Holmes' lack of those "strong emotions" a rightness, because Holmes' activities and even his very nature are incompatible with such things.
Of course, these observations in the first paragraph make the relation to Irene Adler so intriguing, as Watson absolutely insists there was no love there, yet something about her forever captured Holmes' attention. In truth, Adler must have intrigued the readers, as well, as this story is the only one in which she appears and yet countless Sherlock Holmes adaptations feature her prominently.