Holmes uses deduction and footwork to solve the mystery of the Red-Headed League. At first, it does not seem as though a crime has been committed at all. The League is so ridiculous, though, that Holmes is suspicious. He knows that there is something there if he digs a little deeper.
Holmes has his own methods, which often involve thinking. First, he smokes a pipe for fifty minutes, and then he goes to a German music concert to “introspect” (p. 12). Then he goes to the client’s shop and meets the mysterious clerk, whom he recognizes as “the fourth smartest man in London” and the third most daring (p. 13).
Holmes observes the knees of his trousers, and deduces that he has been kneeling. He tests the theory by tapping the sidewalk with his stick. He concludes that the suspect has been digging. He realizes that since there is a bank next door to the shop, the bank is about to be robbed.
Holmes arranges for the police to lie in wait for the suspects to break through, and he also waits (along with Watson), to apprehend the criminals.
“There are three men waiting for him at the door,” said Holmes.
“Oh, indeed! You seem to have done the thing very completely. I must compliment you.” (p. 17)
In the end, the case is rather simple. The criminal James Clay simply concoted a scheme to get the client out of the shop so he could break into the bank.