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.
Eliezer Yudkowsky once wrote that
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.