Sherlock Holmes may be a rationalist, but his process is invisible to the reader.
A typical Holmes conversation (in form, at least):
Lestrade walks in.
SH: From your appearance, I can tell you just came from the morgue.
L: Gadzooks. You are correct. How did you know?
SH: I smell (some chemical) on your clothes. Also, the leather in your shoes is discolored as if (some other chemical) has dripped on it. The only places that use those two chemicals are (some ridiculous industrial location) and the morgue. Since you are a police officer, the logical conclusion is that you have just left the morgue.
But all Holmes' facts (except that Lestrade is a police officer) are invisible to the reader. Also invisible to the reader are the facts about Lestrade that are irrelevant to the story or the analysis (i.e. Lestrade was wearing a brown jacket, he recently shaved, and is carrying a note in his pocket, probably a list of items his wife wants him to buy on the way home).
Even if we wanted to, we couldn't follow along with Holmes' reasoning, including the dismissal of the irrelevant facts. In short, Holmes' "rationality" is really deus ex machina in favor of a character in a story.
I have some magician/"psychic" friends, and so much of that is cold reading (which is pretty much what Sherlock does) and other Dark Arts.
In case people haven't heard of it:
Cold reading is a series of techniques used by mentalists, psychics, fortune-tellers, illusionists, and con artists to determine or express details about another person, often in order to convince them that the reader knows much more about a subject than they actually do.[1] Without prior knowledge of a person, a practiced cold reader can still quickly obtain a great deal of information about the subject by analyzing the person's body language, age, clothing or fashion, hairstyle, gender, sexual orientation, religion, race or ethnicity, level of education, manner of speech, place of origin, etc. Cold readers commonly employ high probability guesses about the subject, quickly picking up on signals from their subjects as to whether their guesses are in the right direction or not, and then emphasizing and reinforcing any chance connections the subjects acknowledge while quickly moving on from missed guesses.
-From wikipedia
There's another massively important step: Check for alternative hypotheses. It's easy to think of explanations for observations, but usually they can have multiple meanings.
This is what CIA research has confirmed--that hypothesizing is easy, but staying open to new ideas after you think you already know the answer is hard (and undervalued).
Edited to add: This is also the topic of Hold Off On Proposing Solutions.
How to Draw Conclusions Like Sherlock Holmes
Engage slow motion mode and run an annotated physics simulation in your mind.
Oh, and the painting I mentioned at the beginning? I actually didn't figure it out until she told me. I just about kicked myself when I realized I could have figured it out myself and pulled off a really cool Sherlock Summation if I hadn't asked first. C'est la vie.
Hindsight bias!
Maybe my old comment on Rationalist Fiction is worth reposting here.
"In defense of Conan Doyle, Wikipedia says:
Sherlock Holmes remains a great inspiration for forensic science, especially for the way his acute study of a crime scene yields small clues as to the precise sequence of events... All of the techniques advocated by Holmes would later become reality, but were generally in their infancy at the time Conan Doyle was writing.
and goes off to claim that later detective fiction actually became less realistic as writers shifted attention to psychology rather than forensics."
How to Draw Conclusions Like Sherlock Holmes? Become a fictional character and point out all the details your author has included to move the plot forward.
Eliezer Yudkowsky once wrote that
[...] when you look at what Sherlock Holmes does - you can't go out and do it at home. Sherlock Holmes is not really operating by any sort of reproducible method. He is operating by magically finding the right clues and carrying out magically correct complicated chains of deduction. Maybe it's just me, but it seems to me that reading Sherlock Holmes does not inspire you to go and do likewise. Holmes is a mutant superhero. And even if you did try to imitate him, it would never work in real life.
A few days ago I was at an acquaintance's house after watching the Sherlock miniseries on Netflix. My mind whirling with the abilities displayed by the titular character and I wandered around the house while others were making small talk. I stopped by a large oil painting on one wall that was decent but had obvious problems with perspective. Additionally, it was missing a signature in the lower-right corner.
ANALYSIS:
Sub-par paintings don't generally get put on the market.
If the hostess thought it was worth putting on the wall, it was most likely because she had an emotional attachment to the piece.
Painters place their signatures in the corner of the painting to identify themselves as the creator. If the painter didn't bother leaving their mark, it was because they were confident that they didn't need to.
The conclusion I drew from this was that the painter was either the hostess herself or somebody very close to her. As it turns out, it was the hostess.
Now, this anecdote hardly proves anything. Still, I think it's a fun little thing and the ability to show off like that, even a small percentage of the time, is too good to pass up. So I present my analysis of How to Become a Regular Sherlock Holmes.
1) Pay attention to details. Look around you at your environment. A scratch on a wall, a limp in somebody's walk, a smudge on somebody's cheek. At this point it's probably hard to tell what details are important, so pay attention to everything.
2) Answer these two questions:
"What am I looking at?" and
"What could it mean (if anything)?"
3) Check your guesses.
This is an important step. It's easy to make any sort of judgments about the details and what they mean, but if you accept your own conclusions without checking the facts, you're likely to create false assumptions and associations that you take as fact. That's the opposite of what we're trying to do here.
Fortunately, checking your guesses is very easy to do in most situations with another person. Just state what you've noticed and ask for information on the context. For example, "I've noticed a large scratch on your end-table. Do you know how it happened?"
A follow-up question might be "why haven't you changed it out for another one?", but only if you think getting the information is more important than the possibility of being seen as rude and the potential consequences thereof.
In Summary:
Pay attention to details
"What am I looking at?"
"What could it mean?"
Check your guesses
Oh, and the painting I mentioned at the beginning? I actually didn't figure it out until she told me. I just about kicked myself when I realized I could have figured it out myself and pulled off a really cool Sherlock Summation if I hadn't asked first. C'est la vie.