First of all, what Sherlock Holmes practices is inductive reasoning and only rarely deductive reasoning. Deductive reasoning is when you take a series of general statements and draw a logically certain conclusion.
All women enjoy shopping,
therefore shopping is all women think about.
Inductive reasoning is a conclusion reached from specific examples
His shirt collar has lipstick on it; he must be having an affair
This is further confused by mathematical induction which is a form of deductiHouasoning. Holmes sometimes deduces and sometimes induces.
1. When Sherlock Holmees describes Dr James Mortimer, by looking at his walking stick
“So your grave, middle aged practitioner vanished into thin air, my dear Watson, there emerges a young fellow under thirty, amiable, unambitious, absent-minded, and the possessor of a favourite dog, which I should describe roughly as as being larger than a terrier and smaller than a mastiff.
“The dog has been in the habit of carrying this stick behind his master. Being a heavy stick the dog has held it tightly by the middle, and the marks of his teeth are very plainly visible. The dog's jaw, as shown in the space between these marks, is too broad in my opinion for a terrier and not broad enough for a mastiff. It may have been – yes, by Jove it is a curly-haired spaniel.”
2. When Sherlock Holmes figures out which newspaper the words were cut from and what sort of person sent the anonymous note
“There is as much difference to my eyes between the loaded bourgeois type of a Time article and the slovenly print of an evening half penny paper as there could be between your negro and your Esquimaux. I confess that once when I was very young I confused the Leeds Mercury with the Western Morning News. But a Times leader is entirely distinctive, and these words could have been taken from nothing else.
“The address, you observe, is is printed in rough characters. But The Times is a paper which is seldom found in any but in the hands but those of the highly educated. We may take it, therefore, that the letter was composed by an educated man who wished to pose as an uneducated one.”
3. When Sherlock Holmes explains how he immediately knew, without looking, that it was Watson inside the hut on the moors
“I could not undertake to recognise your footprint amid all the footprints in the world. If you seriously desire to deceive me you must change your tobacconist; for when I see the stub of a cigarette marked Bradley, Oxford Street, I know that my friend Watson is in the neighbourhood.”
4. When Sherlock Holmes describes how he found out the true identities of Jack and Beryl Stapleton
“He so far forgot himself as to tell you a true piece of autobiography upon the occasion when he first met you and I dare say he had many a time regretted it since. He was once a schoolmaster in the North of England. Now, there is no one more easy to trace than a schoolmaster.
“A little investigation show me that a school had come to grief under atrocious circumstances and that the man who had owned it – the name was different – had disappeared with his wife.
“When I learned that the missing man was devoted to entomology the identification was complete.”
5. When Sherlock Holmes explains Stapleton's true identity to Watson
“He led me back into the banqueting hall, his bedroom candle in his hand, and he held it up against the time-stained portrait on the wall.
“'Is it like anyone you know?'
“He stood upon a chair, and holding up the light in his left hand, he curved his right arm over the broad hat, and round the long ringlets.
“'Good heavens!' I cried in amazement.
“The face of Stapleton had sprung out of the canvas.
"Ha, you see it now. My eyes have been trained to examine faces and not their trimmings. It is the first quality of a criminal investigator that he should see through a disguise."
Source: Sherlock Holmes Hound of the Baskervilles