Jabez Wilson is a very thrifty man. As such, he does not subscribe to a newspaper or go out and buy one off a news vendor, although newspapers in those days probably only sold for a penny. Even if he did buy a newspaper he might not have bought the one in which Clay ran the ad about the vacancy in the Red-Headed League. (In "The Adventure of the Blue Carbuncle," Holmes mentions the following newspapers by name: the Globe, Star, Pall Mall, St. James's, Evening News Standard, Echo.) Obviously, Clay bought the newspaper in which he had run the ad and then pretended to have just found it when he showed it to his employer. Clay had to explain quite a lot about the League, since Wilson had never heard of it. Clay ended up escorting Wilson to the office rented for the purpose and introducing him to the man who called himself Duncan Ross, since Ross had probably never seen Wilson and they wouldn't want to hire the wrong man or reject the man they wanted to deceive.
Mr. Wilson learns about the newspaper ad from his new assistant Vincent Spaulding.
When Mr. Wilson comes to Sherlock Holmes to ask him for help in finding out what happened to the Red-headed League, Holmes asks him how he first heard about the advertisement.
The first thing that put us out was that advertisement. Spaulding, he came down into the office just this day eight weeks, with this very paper in his hand, and he says: “‘I wish to the Lord, Mr. Wilson, that I was a red-headed man.’ ”
Spaulding turns out to be the notorious criminal John Clay, as Holmes deduces after talking to Mr. Wilson. He goes to confirm and sees that he is indeed the man he thought, and realizes also that the man is planning to rob the nearby bank and was just trying to get Mr. Wilson out of the shop long enough to dig a tunnel.