Sherlock Holmes was an early version of a super CSI! He solved cases by his keen powers of observation AND by science. He used logic and facts to formulate his hypothesis and then proceeded to gather evidence to prove his theories. Except for Watson and a few others, he was mostly pretty abrupt with people, especially when working on a case. He did not have much patience for people that were stupid and treated them, as well as criminals, with contempt and disdain. With his clients, however, he is solicitous and kind, taking time to explain things. He is also very encouraging to Watson throughout the stories, as Watson improves his own powers of concentration. When Watson is in error, Holmes corrects him in an assertive, but kindly way. "I'm afraid, my dear Watson, that you are in error" instead of "You idiot! How could you miss that?!"
For example, in The Adventure of the Speckled Band, Holmes figured out that a snake was the insturment of death by observing the vent in Helen Stoner's room, the placement of the bed under the vent, etc. When Helen first comes to Holmes for help, he surprises her by telling her that he knows she has come by train that morning. He knows this because he sees mud on her clothing and a train ticket stub in her hand.
In The Hound of the Baskervilles, Holmes explains how he has figured out the entire mystery in the last chapter, down to the most minute detail - for example Sr. Henry's boot. He observed that the first boot did not work because it was new, and the hound could not get a scent from it. This is why another one of Sr. Henry's boots disappeared. Holmes concludes:
The more outré and grotesque an incident is the more carefully it deserves to be examined, and the very point which appears to complicate a case is, when duly considered and scientifically handled, the one which is most likely to elucidate it.
If you read some of the stories available here on eNotes, you can find additional examples of Holmes' power of observation.