How did Sherlock Holmes know the person visiting him was a teacher?

Jabez Wilson, the client in this case, actually isn't a teacher. He is someone about whom Holmes is able to make a number of remarkable deductions based upon his appearance, but Holmes never suggests that he is a teacher. He deduces from the mismatched sizes of the muscles between his right and left hands that he has been a manual laborer in the past; he deduces that he has spent time in China because of a tattoo he has, as well as the fact that he wears a Chinese coin on his watch chain; he deduces that he takes snuff, presumably because it is detectible as a scent, although Holmes never explains this one outright. He can also tell that the client has been doing a lot of writing lately because his cuff is shiny from rubbing against the desk, while the elbow of his other arm has a patch on it where resting on the desk had worn it smooth. And, indeed, Holmes is quite right about all these things, as Wilson confirms, although he thinks them less miraculous once they are explained to him (to Holmes's chagrin). Wilson has, in fact, been doing a lot of writing on the orders of the so-called Red Headed League, a cover for a criminal gang which Holmes will later expose.

In "The Red-Headed League," the person visiting Sherlock Holmes isn't a teacher—he's a writer.
The plot centers around Jabez Wilson, a former laborer who is now the owner of a pawn shop of middling success. Wilson is approached by his assistant, Spaulding, about a lucrative opportunity for work presented by the so-called "Red-Headed League." Having red hair himself, he inquires about the work. The job is busywork that pays far beyond the actual skill required to do it, specifically, four pounds per week to hand-write a copy of the Encyclopedia Britannica. 
When Wilson arrives at Holmes's Baker Street abode, Holmes makes a number of deductions on sight—Wilson's history as a laborer, his travel to China, and, of course, his role as a writer. Holmes makes this deduction from Wilson's sleeves—the right hand, Wilson's writing hand, is "shiny" in the cuff of his shirt, and the left elbow has a worn spot from where Wilson rested it on his desk.